Koszul spaces

Alexander Berglund

doi:10.1090/S0002-9947-2014-05935-7

Koszul spaces

Alexander Berglund

Department of Mathematical Sciences

10 Citations (Scopus)

Abstract

We prove that a nilpotent space is both formal and coformal if and only if it is rationally homotopy equivalent to the derived spatial realization of a graded commutative Koszul algebra. We call such spaces Koszul spaces and show that the rational homotopy groups and the rational homology of iterated loop spaces of Koszul spaces can be computed by applying certain Koszul duality constructions to the cohomology algebra.

Original language	English
Journal	Transactions of the American Mathematical Society
Volume	366
Issue number	9
Pages (from-to)	4551-4569
ISSN	0002-9947
DOIs	https://doi.org/10.1090/S0002-9947-2014-05935-7
Publication status	Published - 2014

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10.1090/S0002-9947-2014-05935-7

http://arxiv.org/abs/1107.0685

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AB - We prove that a nilpotent space is both formal and coformal if and only if it is rationally homotopy equivalent to the derived spatial realization of a graded commutative Koszul algebra. We call such spaces Koszul spaces and show that the rational homotopy groups and the rational homology of iterated loop spaces of Koszul spaces can be computed by applying certain Koszul duality constructions to the cohomology algebra.

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JO - Transactions of the American Mathematical Society

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Koszul spaces

Abstract

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