Volume rigidity and algebraic shifting

Denys Bulavka; Eran Nevo; Yuval Peled

doi:10.1016/j.jctb.2024.09.002

Volume rigidity and algebraic shifting

Denys Bulavka
, Eran Nevo
, Yuval Peled

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in R^d−1, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is not characterized by a corresponding hypergraph sparsity property.

Original language	English
Pages (from-to)	189-202
Number of pages	14
Journal	Journal of Combinatorial Theory. Series B
Volume	170
DOIs	https://doi.org/10.1016/j.jctb.2024.09.002
State	Published - Jan 2025

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

Algebraic Shifting
Rigidity theory
Simplicial Complexes

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10.1016/j.jctb.2024.09.002

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abstract = "We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in Rd−1, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is not characterized by a corresponding hypergraph sparsity property.",

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doi = "10.1016/j.jctb.2024.09.002",

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AB - We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in Rd−1, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is not characterized by a corresponding hypergraph sparsity property.

KW - Algebraic Shifting

KW - Rigidity theory

KW - Simplicial Complexes

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JF - Journal of Combinatorial Theory. Series B

ER -

Volume rigidity and algebraic shifting

Abstract

Bibliographical note

Keywords

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