Discrete Morse theory for symmetric Delta-complexes

We generalize Forman’s discrete Morse theory to the context of symmetric $\mathrm{\Delta }$-complexes. As an application, we prove that the coloop subcomplex of the link of the origin $L{A}_g^{\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p},\mathrm{P}}$ in the moduli space of principally polarized tropical abelian varieties of dimension $g$ with respect to the perfect cone decomposition is contractible.