Algebra/Topology Seminar

Speaker: Alex Takeda

Title: Categorical coalgebras, homology manifolds and loop co/products

Abstract: In this talk I will describe how to use the formalism of categorical coalgebras (or dg cocategories) and their cobar dg categories to define algebraic analogues of some string topology operations. The data that goes into this definition is a simplicial complex endowed with a certain local type of Poincaré duality structure studied by Ranicki. I will explain how, in the case of a simplicial complex obtained from a triangulated homology manifold, this gives equivalent operations to those defined geometrically; this proof uses certain models for chains on path spaces with homotopy cocommutativity and Hopf structures. Time allowing I will explain how this extension to objects that are not manifolds opens the way to study its dependence on homotopies more directly. This is joint work with Manuel Rivera.