2 papers
math.AT2026
Discrete homotopy hypothesis for n-types
Daniel Carranza, Chris Kapulkin
We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse…
cs.CG2025
Fast computation of the first discrete homology group
Jacob Ender, Chris Kapulkin
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significant…