Summer School on the
Interactions between Homotopy Theory and Algebra
University of Chicago
July 26 to August 6, 2004

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Students who meet the following prerequisites will benefit the most from the summer school. A majority of these topics would be covered in a one semester course in algebraic topology and a one semester course in commutative algebra. Some topics are slightly more advanced though, and students will probably find it beneficial to review this background material before the summer school.


Algebraic Topology: Familiarity with topological spaces, continuous maps, connectivity, homotopic maps, the fundamental group, covering spaces, cell complexes, homology (singular and cellular and the equivalence between the two), the Eilenberg-Steenrod axioms, and calculations of homology groups and some applications such as the fixed point theorem.

Commutative Algebra: Familiarity with rings, ideals, modules, primary decompositions, Spec, localization, local rings, dimension theory, regular sequences, and Koszul complexes.

Homological Algebra: Familiarity with chain complexes, the long exact homology sequence, the snake lemma, Tor and Ext, easy calculations of Tor and Ext (universal coefficient theorems), some more complicated calculations of Tor and Ext over rings other than Z, resolutions (projective/injective), and comparison of resolutions.

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