Séminaire Lotharingien de Combinatoire, 89B.14 (2023), 12 pp.

Denys Bulavka, Eran Nevo and Yuval Peled

Volume Rigidity and Algebraic Shifting

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.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

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