Blake Whiting

Date: February 23, 2024
Time: 12:00 pm - 1:00 pm
Location: ICT 616

Title: Acyclic models

Abstract: Acyclic models, as its commonly seen today, is a proof technique used to show when two chain complexes are chain equivalent or have isomorphic homology. It originated as a theorem by Eilenberg and MacLane (1953), where it was immediately used to show the Eilenberg-Zilber theorem (1953). This theorem, proven directly via acyclic models, gives us a Künneth theorem and defines the cup product, which turns cohomology into a graded ring.

This talk will be an exposition on (one version of) the acyclic models theorem, as given by Michael Barr in 2002. I will give the necessary definitions to understand Barr’s modern formulation of acyclic models, and then prove it. I will assume basic knowledge of chain complexes, but that will be briefly reviewed. Time permitting, I will also discuss how the Eilenberg-Zilber theorem follows directly from it and potential avenues to generalizing acyclic models.

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