Work

Discrete homotopy of graphs and $k$-parabolic subspace arrangements

Year: 2026

Type: preprint

Abstract: Discrete homotopy theory is a combinatorial homotopy theory defined for discrete objects. Barcelo--Severs--White conjectured that the homotopy groups of complements of $k$-parabolic subspace arrangements are isomorphic to the discrete homotopy groups of graphs associated with the Coxeter complexes. We show that this correspondence fails in general by giving a counterexample in degree two for the $4$-parabolic subspace arrangement of type $A_5$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29690

Author: Yamagata, So

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

OpenAlex ID: W7223244100

Cites: 4

Cited by:

Related to: 10