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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



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.

20454?type=thumb Ayala.Notes 417 KB application/pdf Download
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