CW-resolutions of monomial ideals that are supported on face posets

TL;DR

This paper constructs CW-complexes supporting minimal free resolutions of monomial ideals, ensuring the face poset also supports the resolution, with implications for algebraic and topological combinatorics.

Contribution

It introduces a method to build CW-complexes with face posets supporting monomial ideal resolutions, extending previous support conditions to face posets.

Findings

Constructed a CW-complex Y supporting the resolution

Ensured the face poset P(Y) supports the resolution

Applicable to ideals supported on complexes with regular 2-skeletons

Abstract

Given a monomial ideal $I$ with minimal free resolution $\mathcal{F}$ supported in characteristic $p>0$ on a CW-complex $X$ with regular $2$-skeleton, we construct a CW-complex $Y$ that also supports~$\mathcal{F}$ and such that the face poset $P(Y)$ also supports $\mathcal{F}$ in the sense of Clark and Tchernev.