Description:

Title: String topology and the coHochschild complex

Abstract: I will describe a tractable chain-level model for the free loop space of a simplicial complex. The construction is based on a Hochschild homology theory for coalgebras and does not assume any restrictions on the fundamental group or the commutative ring of coefficients. When the underlying simplicial complex is equipped with a local intersection product (e.g. the case of a homology manifold), I will give explicit formulas for string topology operations in terms of this algebraic model; these are operations constructed by intersecting, concatenating, and splitting chains. The formulas use local higher homotopies controlling the compatibility of intersections with the diagonal approximation coproduct.