String topology coproduct: geometric and algebraic aspects of chain constructions (Manuel Rivera)

Ciencias TVJue, noviembre 10, 2016 7:02pmURL:
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String topology coproduct: geometric and algebraic aspects of chain level constructions

Plática dada por Manuel Rivera (Miami-Cinvestav) en el evento Algebraic Geometry in Mexico 2016 el miércoles 1 de noviembre del 2016.

Abstract:
The string topology coproduct is an intersection type operation, originally described by Goresky-Hingston and Sullivan, which considers transversal self intersections on chains of loops in a smooth manifold and splits loops at these intersection points. The geometric chain level construction of string topology operations involves deforming chains to achieve certain transversality conditions and these deformations introduce higher homotopy terms for algebraic compatibilities and properties. The chain level theory for the coproduct is much more subtle and mysterious than for other string topology operations. I will describe joint work with Dingu Yang (IAS) in which we propose a framework and tools for constructing explicitly these operations. I will also present some new results in a parallel project with Zhengfang Wang (IMJ-PRG) in which we describe a single BV-algebra that combines the algebraic analogues of the coproduct and the Chas-Sullivan loop product in Hochschild complexes of Frobenius algebras.