Daniel Carranza, Johns Hopkins University
 
Hurewicz Theorem in Discrete Homotopy Theory

Tuesday, Nov 14th, 10:00am

Abstract: Homotopy groups, while easy to define, are notoriously hard to compute (both for spaces and graphs). By contrast, homology groups are much more computable, despite their more complicated definition. One would like a way of leveraging homological techniques to compute homotopy groups, and in classical algebraic topology, this is achieved by means of the Hurewicz theorem. This theorem states that for a connected space, the first non-trivial homotopy and homology groups agree (up to abelianization). I will present a discrete analogue of this theorem, and show how it can be used to compute previously-unknown higher homotopy groups of graphs. This talk is based on joint work with Chris Kapulkin (arXiv:2202.03516).