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Polynomial filling functions of sublevel sets in CAT(0) cube complexes
Abstract
We give a criterion ensuring that sufficiently high sublevel sets of a discrete Morse function on a CAT(0) cube complex have polynomial integral homological filling functions. As one application, we verify this criterion for the Stein--Farley complexes of the Higman--Thompson groups Fd,r, Td,r, and Vd,r. Consequently, these groups have polynomial homological filling functions in every degree k≥2.
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BibTeX
@misc{weis2026polynomial,
title = {{Polynomial filling functions of sublevel sets in $\mathrmCAT(0)$ cube complexes}},
author = {Jannis Weis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06276},
eprint = {2610.06276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06276},
}
RIS
TY - UNPB
TI - Polynomial filling functions of sublevel sets in CAT(0) cube complexes
AU - Jannis Weis
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06276
UR - https://arxiv.org/abs/2610.06276
AB - We give a criterion ensuring that sufficiently high sublevel sets of a discrete Morse function on a CAT(0) cube complex have polynomial integral homological filling functions. As one application, we verify this criterion for the Stein--Farley complexes of the Higman--Thompson groups F_d,r, T_d,r, and V_d,r. Consequently, these groups have polynomial homological filling functions in every degree k≥2.
ER -