Scott Wilson
University of Minnesota
The Algebra of Chains
Abstract: One way to understand an algebraic structure on the chains
of a space or a manifold is to relax the condition on where the
algebraic structure is defined. In particular, much is gained by
reducing or enlarging either the domain or range of the
operations. I'll describe such "partially defined algebraic
structures" abstractly, and give examples related to the classical
diagonal map and intersection product. Together we'll see how, for a
manifold, these two fit together to give a (partial) chain-level open
Frobenius algebra. This is recent joint work with G. Friedman and
J. McClure, building off work of Goresky-MacPherson, McClure and ideas
of Sullivan on open Frobenius algebras.