Claremont Topology Seminar: Iris Yoon (Wesleyan University)

We especially welcome all undergraduates and graduate students to attend topology seminar!

Speaker: Iris Yoon (Wesleyan University)

Title: Dowker duality, profunctors, and spectral sequences

Abstract: I will present three short, new proofs of Dowker duality using various poset fiber lemmas. I will introduce modifications of joins and products of simplicial complexes called relational join and relational product complexes. These relational complexes can be constructed whenever there is a relation between simplicial complexes, which includes the context of Dowker duality and covers of simplicial complexes. In this more general setting, I will show that the homologies of the simplicial complexes and the relational complexes fit together in a long exact sequence. If time permits, I’ll discuss similar results for profunctors, which are generalizations of relations to categories.