Which Properties of Stanley–Reisner Rings and Simplicial Complexes are Topological?

Volkmar Welker ()
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Volkmar Welker: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg

A chapter in Commutative Algebra, 2021, pp 859-889 from Springer

Abstract: Abstract In this article we survey results on topological properties of simplicial complexes Δ, mostly defined via algebraic properties of its Stanley-Reisner ring 𝕂 [ Δ ] $$\mathbb {K}[\Delta ]$$ . A property of Δ or 𝕂 [ Δ ] $$\mathbb {K}[\Delta ]$$ is called topological if it only depends on the homeomorphism type of the geometric realization of Δ (and on 𝕂 $$\mathbb {K}$$ ).

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_27

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DOI: 10.1007/978-3-030-89694-2_27

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