Koszulity of splitting algebras associated with cell complexes ☆ ☆ Some of our results were later generalized by T. Cassidy, C. Phan, and B. Shelton in their paper “Noncommutative Koszul algebras from combinatorial topology” in arXiv:0811.3450

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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Bibliographic Details
Published in:Journal of algebra 2010-02, Vol.323 (4), p.983-999
Main Authors: Retakh, Vladimir, Serconek, Shirlei, Wilson, Robert Lee
Format: Article
Language:English
Subjects:
Cell decompositions
Koszulity
Splitting algebras
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2009.11.039