CONTRACTIBILITY OF THE ORBIT SPACE OF THE p-SUBGROUP COMPLEX VIA BROWN-FORMAN DISCRETE MORSE THEORY

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].

Automated summary

We provide a concise proof for the contractibility of the orbit space of the p-subgroup complex of a finite group, employing Brown-Forman discrete Morse theory. This result was first conjectured by Webb and later proved by Symonds.