Higher Nerves of Simplicial Complexes

We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of the Stanley-Reisner ring \(k[\Delta]\) as well as the \(f\)-vector and \(h\)-vector of \(\Delta\). We present, as an appl...

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Published in:arXiv.org 2019-01
Main Authors: Dao, Hailong, Doolittle, Joseph, Duna, Ken, Goeckner, Bennet, Holmes, Brent, Lyle, Justin
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Language:English
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Homology
Nerves
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creator Dao, Hailong
Doolittle, Joseph
Duna, Ken
Goeckner, Bennet
Holmes, Brent
Lyle, Justin
description We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of the Stanley-Reisner ring \(k[\Delta]\) as well as the \(f\)-vector and \(h\)-vector of \(\Delta\). We present, as an application, a formula for computing regularity of monomial ideals.
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subjects Homology
Nerves
title Higher Nerves of Simplicial Complexes
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