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\def\splin{{\rm SL}}
\def\R{{\bf R}}
\def\scrf{{\cal F}}
	
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\centerline{PUBLICATION LIST}
\centerline{Scot Adams}
\centerline{\today}
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\noindent

\vskip.25in\noindent
1. Locally free actions on Lorentz manifolds, preprint.

\vskip.1in\noindent
If a topological group $G$ acts on a topological space $M$,
then we say that the
action is {\it orbit nonproper}
provided that, for some $m_0\in M$,
the orbit map $g\mapsto gm_0:G\to M$ is nonproper.
Let $\scrg$ be the collection of connected Lie groups $G$ such
that either $G$ has simply connected nilradical or $G$ is the
connected real points of an algebraic $\R$-group.
In this paper,
we characterize the groups in $\scrg$ which admit a
locally free, orbit nonproper action by isometries of a Lorentz
manifold. We also consider what happens when ``locally free'' is
replaced by the weaker condition that the connected component of the
identity of any stabilizer is compact.

\vskip.25in\noindent
2. Isometric actions of ${\rm SL}_n(\R)\ltimes\R^n$ on Lorentz manifolds,
with Garrett Stuck, preprint.

\vskip.1in\noindent
We prove that, for $n\ge3$, a locally faithful action of
${\rm SL}_n(\R)\ltimes\R^n$ by isometric transformations
of a Lorentz manifold must be a proper action.

\vskip.25in\noindent
3. Conformal actions of ${\rm SL}_n(\R)$ and
${\rm SL}_n(\R)\ltimes\R^n$ on Lorentz manifolds,
with Garrett Stuck, to appear,
{\it Transactions of the American Mathematical Society}.

\vskip.1in\noindent
We prove that, for $n\ge3$, a locally faithful action of
${\rm SL}_n(\R)$ or of ${\rm SL}_n(\R)\ltimes\R^n$
by conformal transformations of a Lorentz manifold
must be a proper action.  

\vskip.25in\noindent
4. Amenable isometry groups of Hadamard spaces, with Werner Ballmann,
accepted, {\it Mathematische Annalen}.

\vskip.1in\noindent
We prove that an amenable group of isometries of a locally
compact Hadamard space either fixes a point at infinity, or
fixes a flat subspace.

\vskip.25in\noindent
5. Another proof of Moore's ergodicity theorem for ${\rm SL}(2,\R)$,
{\it Contemporary Mathematics}, {\bf215} (1998), 183-187.

\vskip.1in\noindent
We present Ellis and Nerurkar's proof of Moore's ergodicity
theorem for ${\rm SL}(2,\R)$. No background on the Ellis-Nerurkar
enveloping semigroup is needed to understand this exposition.

\vskip.25in\noindent
6. The isometry group of a compact Lorentz manifold, I,
with Garrett Stuck, {\it Inventiones Mathematic\ae},
{\bf129} (1997), 239-261.

\vskip.1in\noindent
We classify the connected Lie groups that can act
locally faithfully and isometrically on a compact Lorentz manifold.  

\vskip.25in\noindent
7. The isometry group of a compact Lorentz manifold, II,
with Garrett Stuck, {\it Inventiones Mathematic\ae},
{\bf129} (1997), 263-287.

\vskip.1in\noindent
We classify the Lie groups that are isomorphic to the universal
cover of the connected component of the identity of
the isometry group of a compact connected
Lorentz manifold.  

\vskip.25in\noindent
8. A foliated metric rigidity theorem
for higher rank irreducible symmetric spaces,
with L.~Hernandez,
{\it Geometric and Functional Analysis (GAFA)},
{\bf4} no.~5 (1994), 483-521.

\vskip.1in\noindent
Let $\scrf$ be a foliation of a compact manifold with a transverse
invariant measure of finite total mass.
We prove that if $\scrf$ admits a leafwise metric
such that every leaf is an irreducible symmetric space
of noncompact type and higher rank, then
any other leafwise metric of nonpositive curvature
is also symmetric along any leaf in the support of the
transverse measure.
A rank one version of this result is also exposed.

\vskip.25in\noindent
9. Reduction of cocycles with hyperbolic targets,
{\it Ergodic Theory and Dynamical Systems}, {\bf16} (1996), 1111-1145.

\vskip.1in\noindent
I show that any cocycle from an ergodic, finite measure preserving
action of a higher rank group to a closed subgroup of the
isometry group of a proper, geodesic hyperbolic,
``at most exponential'' metric
space is necessarily cohomologous to a cocycle with values
in a compact subgroup. Philosophically, this says that
higher rank dynamics is incompatible with hyperbolic
dynamics; since hyperbolicity is, in some sense, generic
among finitely presented groups,
this places strong restrictions on the possible dynamics
of higher rank groups.
We derive some applications of the main result.
When the target group of the cocycle
has no small subgroups, we show that
the main result holds for a wider class of domain groups.

\vskip.25in\noindent
10. Some new rigidity results for stable orbit equivalence,
{\it Ergodic Theory and Dynamical Systems}
{\bf15} (1995), 209-219.

\vskip.1in\noindent
Broadly speaking, I prove that an action of a group with very little
commutativity cannot be stably orbit equivalent to an action
of a group with enough commutativity,
assuming both actions are free and finite measure preserving.
For example, one group
may be $\splin_2(\R)$ and the other a group with infinite discrete
center ({\it e.g.}, the universal cover of $\splin_2(\R)$); I believe
this is the first rigidity result of this type for a pair of
simple Lie groups both of split rank one.
Another example: one group may be any
nonelementary word hyperbolic group, the other any group
with infinite discrete center.

\vskip.25in\noindent
11. Splitting of nonnegatively curved leaves in minimal sets
of foliations, with G.~Stuck, {\it Duke Mathematical Journal}
{\bf71} no.~1 (1993), 71-91.

\vskip.1in\noindent
\def\scrf{{\cal F}}
We show that if $\scrf$ is a foliation of a compact Riemannian
manifold, if $L$ is a leaf in a minimal set of $\scrf$
and if $L$ has nonnegative Ricci curvature (in the inherited metric),
then the universal cover of $L$ splits isometrically
as the product of a compact manifold and a flat Euclidean space.
In the process, we develop a method of relating the study
of minimal sets in foliations of Riemannian manifolds
to the study of minimal actions of Lie groups.
We record some geometric consequences of the splitting theorem.

\vskip.25in\noindent
12. Amenable actions of groups,
with G.~Elliott and T.~Giordano,
{\it Transactions of the American Mathematical Society}
{\bf344} no.~2 (August 1994), 803-822.

\vskip.1in\noindent
We prove that a nonsingular action of a locally compact group
on a measure space is amenable iff there is a global invariant mean
iff a.e.~stabilizer is amenable and the underlying equivalence
relation is amenable. This extends results of R.~Zimmer and of
G.~Elliott and T.~Giordano from discrete groups to locally compact
groups. It is a corollary of this result that an action is
amenable iff a.e.~ergodic component is. Zimmer proved that
any extension of an ergodic amenable action is again amenable;
we may now remove the ergodicity assumption from that statement.
We also demonstrate that an action is amenable iff it is the
Mackey range of a homomorphism from an amenable countable equivalence
relation iff it is the Posson boundary of a group-invariant
matrix-valued Markov random walk on $G$.

\vskip.25in\noindent
13. Betti numbers of congruence groups, with P.~Sarnak and
with an appendix by Z.~Rudnick, {\it Israel Journal of Mathematics}
{\bf88} (1994), 31-72.

\vskip.1in\noindent
We show, for certain congruence families of Galois
coverings of a manifold, that the individual Betti numbers are
polynomial periodic functions of the level. We prove similar
results for the dimensions of other spaces of automorphic
forms.

\vskip.25in\noindent
14. Representation varieties of arithmetic groups
and polynomial periodicity of Betti numbers,
{\it Israel Journal of Mathematics}
{\bf88} (1994), 73-124.

\vskip.1in\noindent
I give a method of studying character varieties of
arithmetic groups with an application to polynomial periodicity of
Betti numbers of manifolds in congruence towers.

\vskip.25in\noindent
15. Boundary amenability for word hyperbolic groups
and an application to smooth dynamics of simple groups,
{\it Topology} {\bf 33} no.~4 (1994), 765-783.

\vskip.1in\noindent
Let $\Gamma$ be a finitely generated group which is hyperbolic
in the sense of Gromov. I prove that the action of $\Gamma$ on
its boundary is amenable with respect to any quasi-invariant
measure. I give an application of this result to actions
of higher rank simple Lie groups on smooth manifolds.

\vskip.25in\noindent
16. Indecomposability of equivalence relations
generated by hyperbolic groups,
{\it Topology} {\bf 33} no.~4 (1994), 785-798.

\vskip.1in\noindent
Let $\Gamma$ be a finitely generated group which is hyperbolic
in the sense of Gromov. Assume $\Gamma$ is not amenable.
I prove that a free, finite measure preserving action of $\Gamma$
yields an equivalence relation which cannot be written measurably as
a product of two measured equivalence relations, unless
one of the two relations has finite equivalence classes.
I obtain a natural extension of this result to the quasi-measure
preserving case.

\vskip.25in\noindent
17. Rank rigidity for foliations by manifolds of nonpositive
curvature,
{\it Differential Geometry and Its Applications}
{\bf3} (1993), 47-70.

\vskip.1in\noindent
I prove a rank rigidity theorem for finite volume foliations
by manifolds of nonpositive sectional curvature. It implies
that if the leaves are irreducible Hadamard manifolds of geometric rank
$\ge2$, then the leaves are symmetric.

\vskip.25in\noindent
18. An application of the Very Weak Bernoulli condition
for amenable groups, with J.~Steif,
{\it Pacific Journal of Mathematics}
{\bf159} no.~1 (1993), 1-17.

\vskip.1in\noindent
In this paper, we give an application of the
Very Weak Bernoulli condition for amenable groups.
(See the paper ``Very Weak Bernoulli for amenable groups''
described below.) The setting for the application 
is an attractive particle system with the usual lattice
replaced by a general countable amenable group.

\vskip.25in\noindent
19. Amenability, Kazhdan's property and percolation
for trees, groups and equivalence relations,
with R.~Lyons,
{\it Israel Journal of Mathematics} {\bf75} (1991), 341-370.

\vskip.1in\noindent
We prove amenability for a broad class of
equivalence relations which have trees associated to the equivalence
classes.  The proof makes crucial use of percolation on trees.  We
also discuss related concepts and results, including amenability of
automorphism groups. A second main result is that no discrete subgroup
of the automorphism group of a tree is isomorphic to the fundamental group
of any closed manifold $M$ admitting a nontrivial connection-preserving,
volume-preserving action of a noncompact, simply connected, almost
simple Lie group having Kazhdan's property (T).
The technique of proof also shows that $M$ does not
admit a hyperbolic structure.

\vskip.25in\noindent
20. Nonnegatively curved leaves in foliations,
with A.~Freire,
{\it Journal of Differential Geometry}
{\bf34} (1991), 681-700.

\vskip.1in\noindent
We prove a conjecture of R.~Zimmer which he formulated as the nonnegative
curvature version of his result in [Z1]. He conjectured:
for foliations of measure spaces by Riemannian leaves with
(transverse invariant measure and)
finite total volume, if a.e.~leaf is complete and
has nonnegative Ricci curvature, then a.e.~leaf splits isometrically as the
product of a compact Riemannian manifold and a flat Euclidean space.
The techniques involved are drawn from geometric analysis, especially
from a seminal paper of S.-T.~Yau [Y].
In fact, Zimmer's foliation conjecture has, as a corollary, one of the
most important theorems in Yau's paper:
for complete manifolds of nonnegative Ricci curvature,
finite volume is equivalent to compact.

\vskip.25in\noindent
21. Superharmonic functions on foliations,
{\it Transactions of the American Mathematical Society}
{\bf330} no.~2 (1992), 625-635.

\vskip.1in\noindent
I generalize a result of L.~Garnett. In [G], she proved
that, for a foliation of a compact Riemannian
manifold with (transverse invariant measure and) finite
total volume, any bounded Borel function which is leafwise harmonic
is constant on a.e.~leaf.
This is interesting because it can happen that almost every leaf
is isometric to hyperbolic space and therefore carries
a large number of bounded harmonic functions.
Garnett uses probabilistic techniques. By using techniques
from geometric analysis, I extend this to positive
superharmonic functions. In addition, I prove the result for general
foliations of measure spaces, a broader class of foliations
introduced by R.~Zimmer [Z2].

\vskip.25in\noindent
22. Very Weak Bernoulli for amenable groups,
{\it Israel Journal of Mathematics} {\bf78} (1992), 145-176.

\vskip.1in\noindent
I strengthen F\o lner Independence (defined in
``F\o lner Independence and the amenable Ising model'',
listed next) to a criterion which we call Very Weak Bernoulli.
I prove that this new condition is equivalent to Finitely Determined.

\vskip.25in\noindent
23. F\o lner Independence and the amenable Ising model,
{\it Ergodic Theory and Dynamical Systems}
{\bf12} (1992), 633-657.

\vskip.1in\noindent
I define a criterion called F\o lner Independence
for a stationary process over an amenable group.
Intuitively, a process satisfies the criterion if,
for sufficiently invariant
F\o lner sets, the process in the F\o lner set is nearly
independent of the process outside. I show that F\o lner Independence
implies Finitely Determined.
As an application, I show that, in its extreme Gibbs states,
the amenable attractive Ising model is F\o lner Independent,
(hence Finitely Determined, hence Bernoulli).

\vskip.25in\noindent
24. Kazhdan groups, cocycles and trees,
with R.~Spatzier, partially based on my thesis,
{\it American Journal of Mathematics} {\bf112} (1990), 271-287.

\vskip.1in\noindent
In my thesis (Chicago, 1987), I show that a countable
Kazhdan equivalence relation
(defined by R.~Zimmer) is not ``treeable'' (that is, does not admit
a measurably varying tree-structure on each equivalence class).
The technique of proof can be used to prove a cocycle
analogue of Y.~Watatani's
theorem that Kazhdan's property (T) implies Property (FA) of Serre.
In this paper, R.~Spatzier and I also give a number of other
applications of this ergodic form of Watatani's theorem. In addition,
we prove that Watatani's theorem holds for actions on {\bf R}-trees.
The boundary theory of Morgan-Shalen-Bestvina-Paulin allows us to
conclude compactness of the deformation space of representations of
a discrete Kazhdan group into a rank one semisimple Lie group.

\vskip.25in\noindent
25. Indecomposability of treed equivalence relations, based on thesis,
{\it Israel Journal of Mathematics}
{\bf64} no.~3 (1988), 362-380.

\vskip.1in\noindent
In this paper, I show that if $R$ is a nonamenable, countable,
treeable equivalence relation fixing a finite measure on a measure space,
then $R$ is indecomposable, {\it i.e.}, $R$ is not stably isomorphic
to a product of two equivalence relations.
It then follows that an equivalence relation coming from a free
action of an amalgam of two finite groups over a third is indecomposable.

\vskip.25in\noindent
26. Trees and amenable equivalence relations, based on thesis,
{\it Ergodic Theory and Dynamical Systems}
{\bf10} (1990), 1-14.

\vskip.1in\noindent
This paper contains two main results. The first says that, in a
countable, finite measure preserving treed equivalence relation,
almost every tree must have one or two ends. It is
an analogue to a theorem of R.~Zimmer [Z1] which says that, in an amenable,
finite measure preserving foliation by Hadamard manifolds,
almost every leaf must be flat. The second result is that any
treed equivalence relation with almost every tree of subexponential
growth must be amenable. This corresponds to a well-known result:
amenability of foliations by leaves of polynomial growth.

\vskip.25in\noindent
27. An equivalence relation that is not freely generated
{\it Proceedings of the American Mathematical Society}
{\bf102} no.~3 (1988), 565-566.

\vskip.1in\noindent
In this paper, I answer a question posed by J.~Feldman and C.~Moore
in [FM], one of their two seminal papers on the ergodic theory of countable
equivalence relations.
They ask if any countable Borel equivalence relation on a Borel space is
given by a free action of a countable group of Borel automorphisms.
The answer is no, and a counterexample is constructed by taking
the disjoint union of two equivalence relations, one coming from
a free action of an amenable group, the other coming from a free
action of a nonamenable group.

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\line{\hfil}
\vskip.55in
\centerline{\bf REFERENCES}
\vskip.2in

\vskip.1in
\item{[FM]} Feldman, J.~and Moore, C.,
{\it Ergodic equivalence relations, cohomology,
and von Neumann algebras. I},
Transactions of the AMS {\bf234} no.~2 (1977), 289-324.

\vskip.1in
\item{[G]} Garnett, L.
{\it Foliations, the ergodic theorem and Brownian motion},
Journal of Functional Analysis {\bf51} (1983), 285-311.

\vskip.1in
\item{[OW]} Ornstein, D.~and Weiss B.,
{\it Entropy and isomorphism theorems for actions of amenable groups},
Journal d'Analyse Math\'ematique {\bf 48} (1987), 1-141.

\vskip.1in
\item{[Y]} Yau, S.-T.,
{\it Some function-theoretic properties
of complete Riemannian manifolds and their applications to geometry},
Indiana University Mathematics Journal {\bf25} (1976), 659-670.

\vskip.1in
\item{[Z1]} Zimmer, R.,
{\it Curvature of leaves in amenable foliations},
Amer.~J.~Math {\bf105} (1983), 1011-1022.

\vskip.1in
\item{[Z2]} Zimmer, R.,
{\it Ergodic theory, semisimple Lie groups
and foliations by manifolds of negative curvature},
Publ.~Math.~IHES {\bf 55} (1982), 37-62.

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