Contractibility of the orbit space of the 𝑝-subgroup complex via Brown-Forman discrete Morse theory

Steinberg, Benjamin

doi:10.1090/proc/16688

Contractibility of the orbit space of the $p$-subgroup complex via Brown-Forman discrete Morse theory
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by Benjamin Steinberg;

Proc. Amer. Math. Soc. 152 (2024), 515-519

DOI: https://doi.org/10.1090/proc/16688

Published electronically: November 7, 2023

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Abstract:

We give a simple proof that the orbit space of the $p$-subgroup complex of a finite group is contractible using Brown-Forman discrete Morse theory. This result was originally conjectured by Webb [Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 349–365] and proved by Symonds [Comment. Math. Helv. 73 (1998), pp. 400–405].

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