Cellular cochain algebras and torus actions
Ilia V. Baskakov, Victor M. Buchstaber, Taras E. Panov
TL;DR
This paper establishes an algebraic isomorphism between the integral cohomology of moment-angle complexes and the Tor-algebra of face rings, linking topological and algebraic structures in torus actions.
Contribution
It proves a new isomorphism connecting the cohomology of moment-angle complexes with algebraic Tor computations for face rings.
Findings
Integral cohomology of Z_K is isomorphic to the Tor-algebra of Z[K]
Provides algebraic tools for studying moment-angle complexes
Bridges topological and combinatorial algebraic methods
Abstract
We prove that the integral cohomology algebra of the moment-angle complex Z_K, or of the corresponding coordinate subspace arrangement complement U(K), is isomorphic to the Tor-algebra of the face ring Z[K] of simplicial complex K.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Geometric and Algebraic Topology