The crosscut poset

Abstract

We introduce a new combinatorial invariant, which we call crosscut poset, that is finer than the crosscut complex. We exhibit many applications of the crosscut poset which include a generalization of Björner's crosscut theorem and two results concerning the fixed point property and the fixed simplex property.

12 pages. The arXiv article arXiv:2006.11800v1 has been split into two parts. This article corresponds to the first of those parts