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# *Cancelled* Claremont Topology Seminar: Iris Yoon (Wesleyan College)

## March 19 @ 3:00 pm - 4:00 pm

This talk has been cancelled.

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

~~Speaker: Iris Yoon (Wesleyan College)~~

~~Title: A generalized Dowker complex for multi-way Relations~~

~~Abstract: Given a relation between two sets X and Y, one can construct two simplicial complexes, one having X as its vertex set and the other having Y as its vertex set. These two simplicial complexes (both called Dowker complexes), have initially been shown to have isomorphic homology groups (Dowker, 1952) and were later shown to be homotopy equivalent (Bjorner, 1988). I will present a generalization of the Dowker complex to multi-way relations. The construction is inspired by a new proof of Dowker homotopy equivalence (Brun & Salbu 2023) that embodies Quillen’s Theorem A. I will present different perspectives for understanding the generalized Dowker complex, including as global sections of a cellular cosheaf and as the homotopy colimit of some underlying diagram. This is joint work with many collaborators (Vaupel, Schonsheck, de Silva, Giusti, Sazdanovic, among others), and all results are preliminary.~~