Homological algebra and ...
[ambient page updated Wed, 23 Sep '09, 08:07 AM]
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[ garrett@math.umn.edu ]
[more details later...]
Tentative outline/list of topics
Notes, examples, supplements (Reverse chronological
order. Labels will become links when targets are ready.)
Sample phenomena illustrating homological ideas in nature:
- [ Snake lemma, extensions, Gamma function
]
... [ updated Tue, 23 Jun '09, 12:06 PM]...
... Illustration of extension and uniqueness of
distributions by
simple homological ideas. Easiest example: homogeneous distributions
and Gamma.
- In 2009-2010: MWF 12:20-1:10, Vincent 2 [Room change!]
- Prerequisites: abstract algebra ... and willingness to see examples
and illustrations from all parts of mathematics
- Office hours: MWF after class, email anytime
- To integrate some things whose inter-relations are sometimes
neglected, I will not follow any particular text. Of the sources
listed below, Weibel might be the most relevant, and Eisenbud, both of
these in terms of over-all content rather than logical ordering.
- Some standard sources:
- Weibel Homological Algebra
- Gelfand and Manin Methods of Homological Algebra
- Kashiwara and Shapira Categories and Sheaves
- Hilton and Stambach, Homological algebra
- Cartan and Eilenberg, Homological algebra
- Grothendieck, Tohoku J. paper
- MacLane, Homology
- Eisenbud Commutative Algebra with a View Toward Algebraic
Geometry
- Bourbaki Commutative Algebra
- Atiyah and MacDonald Commutative Algebra
- Zariski and Samuel, Commutative algebra, two volumes
- Milnor Introduction to algebraic K-theory
- Rosenberg Introduction to algebraic K-theory
- Srinivas Algebraic K-theory
- Mitchell Theory of categories
- Freyd Abelian categories
- MacLane Categories for the working mathematician
© 1996-2009,
Paul Garrett
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[ garrett@math.umn.edu
]
[this page is http://www.math.umn.edu/~garrett/m/hom/]
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