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Discrete homotopy of graphs and k-parabolic subspace arrangements

  • So Yamagata
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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 A5.

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Cite

BibTeXRIS
BibTeX
@misc{yamagata2026discrete,
  title = {{Discrete homotopy of graphs and $k$-parabolic subspace arrangements}},
  author = {So Yamagata},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29690},
  eprint = {2610.29690},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29690},
}
RIS
TY  - UNPB
TI  - Discrete homotopy of graphs and k-parabolic subspace arrangements
AU  - So Yamagata
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29690
UR  - https://arxiv.org/abs/2610.29690
AB  - 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.
ER  -