Year: 2025
Type: article
Abstract: The existence of acyclic complete matchings on the face poset of a regular CW complex implies that the underlying topological space of the CW complex is contractible by discrete Morse theory. In this paper, we construct explicitly acyclic complete matchings on any nontrivial Bruhat interval based on any reflection order on the Coxeter group . We then apply this combinatorial result to regular CW complexes arising from the theory of total positivity. As an application, we show that the totally nonnegative Springer fibers are contractible. This verifies a conjecture of Lusztig. As another application, we show that the totally nonnegative fibers of the natural projection from full flag varieties to partial flag varieties are contractible. This leads to a much simplified proof of the regularity property on totally nonnegative partial flag varieties compared to the proofs by Galashin et al. and Bao and He.
DOI: 10.1112/plms.70118
Authors: Huanchen Bao, Xuhua He
Institutions: National University of Singapore, University of Hong Kong
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117656765