Koszulity of splitting algebras associated with cell complexes

2008/10/07 by Vladimir Retakh, Retakh, Vladimir, Shirlei Serconek +3 · 2 citations
Mathematics · #16S37 #55U10 #57M20 #57M60 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.AT #math.RA #msc:16S37 #msc:55U10 #msc:57M20 #msc:57M60

paper · pdf · doi:10.48550/arxiv.0810.1241

Latex, 20 pages, one figure

openalex publication_date 2008/10/07 · arxiv created 2008/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For a two-dimensional manifold M the algebra is Koszul if and only if the Euler characteristic of M is two.

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• From factorizations of noncommutative polynomials to combinatorial topology
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