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Poincare'/Koszul duality and formal moduli

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

April 07, 2014 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): John Francis (Northwestern University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC



For g a dgla over a field of characteristic zero, the dual of the Hochschild homology of the universal enveloping algebra of g *completes* to the Hochschild homology of the Lie algebra cohomology of g.  In this talk we will resolve this completion discrepancy through considerations of formal algebraic geometry.  This will be an instance of our main result, which is a version of Poincare' duality for factorization homology as it interacts with Koszul duality in the sense of formal moduli.  This can be interpreted as a duality among certain topological field theories that exchanges perturbative and non-perturbative.  


20455?type=thumb Francis.Notes 91.6 KB application/pdf Download
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