Kuerak Chung
 	       University of Minnesota

		Based Cacti

Abstract: It is well known that the rational homology of an n-fold
loop space has an n-algebra (or n-Poisson algebra) structure. By
looking this structure together with comultiplication, we define a new
algebraic structure called n-Hopf algebra and show that the rational
homology of n-fold loop space is an n-Hopf algebra. I will give a
structure theorem of n-Hopf algebras in this talk: Any connected
cocommutative n-Hopf algebra is isomorphic to the symmetric algebra of
its primitive part.