Remarks about $Delta$-complexes and applications

摘要

We first consider some generalities regarding $Delta$-complexes, in particular, we give a brief history of the category of $Delta$-complexes, and its relation to the category of semi-simplicial complexes introduced in 1950 by Eilenberg and Zilber. A natural construction of $Delta$-complexes arising from a group action on a simplicial complex is next considered. Finally, an application of this construction to obtain an elementary explicit computation of the cohomology ring $H^{*} (mathbb{R}P^n ; mathbb{Z}_2)$, based on a $Delta$-complex structure, is given.