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Poincaré/Koszul duality

Reimagining the Foundations of Algebraic Topology April 07, 2014 - April 11, 2014

April 07, 2014 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): David Ayala (Montana State University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

What is Poincaré duality for factorization homology? Our answer has three ingredients: Koszul duality, zero-pointed manifolds, and Goodwillie calculus. We introduce zero-pointed manifolds so as to construct a Poincaré duality map from factorization homology to factorization cohomology; this cohomology theory has coefficients the Koszul dual coalgebra. Goodwillie calculus is used to prove this Poincaré/Koszul duality when the coefficient algebra is connected. The key technical step is that Goodwillie calculus is Koszul dual to Goodwillie-Weiss calculus.

Supplements
20454?type=thumb Ayala.Notes 417 KB application/pdf Download
Video/Audio Files

v1315

H.264 Video v1315.mp4 325 MB video/mp4 rtsp://videos.msri.org/data/000/020/393/original/v1315.mp4 Download
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