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Koszul spaces


Author: Alexander Berglund
Journal: Trans. Amer. Math. Soc. 366 (2014), 4551-4569
MSC (2010): Primary 55P62; Secondary 16S37
Published electronically: April 16, 2014
MathSciNet review: 3217692
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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.


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Additional Information

Alexander Berglund
Affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark
Address at time of publication: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
Email: alexb@math.ku.dk

DOI: https://doi.org/10.1090/S0002-9947-2014-05935-7
Received by editor(s): November 18, 2011
Received by editor(s) in revised form: August 8, 2012
Published electronically: April 16, 2014
Additional Notes: This work was supported by the Danish National Research Foundation (DNRF) through the Centre for Symmetry and Deformation
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.