Excisive invariants of manifolds and links
by David Ayala
Abstract: Numerous interesting examples of invariants of 3-manifolds and links satisfy a local-to-global expression. In this talk, we will axiomatize invariants satisfying such an expression and classify them in terms of algebraic data. A few examples will be explicated. The basic construction is an elaboration of configuration spaces with labels. Through this language there is a refinement of Poincar\'e duality which leads to some interesting conclusions.