Brown functors of directed graphs
Organizers
Speaker
Hsuan-Yi Liao
Time
Tuesday, May 20, 2025 2:00 PM - 3:00 PM
Venue
A3-4-312
Online
Zoom 928 682 9093
(BIMSA)
Abstract
In this talk, we consider Brown functors of directed graphs --- that is, contravariant functors from the homotopy category of finite directed graphs to the category of abelian groups, satisfying the triviality axiom, the additivity axiom, and the Mayer-Vietoris axiom. Our main theorem states that such a functor is representable. In addition, we show that the first path cohomology of directed graphs provides a nontrivial example of a Brown functor. This talk is based on joint work with Zachary McGuirk, Dang Khoa Nguyen, and Byungdo Park.