Discrete Morse theory for symmetric Delta-complexes

Abstract

We generalize Forman's discrete Morse theory to the context of symmetric $\Delta$-complexes. As an application, we prove that the coloop subcomplex of the link of the origin $L{A}_g^{\mathrm{trop},\mathrm{P}}$ in the moduli space of principally polarized tropical abelian varieties of dimension $g$ with respect to the perfect cone decomposition is contractible.

16 pages, 5 figures