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Realization spaces of algebraic structures on cochains

Abstract : Given an algebraic structure on the cohomology of a cochain complex , we define its realization space as a Kan complex whose vertices are the structures up to homotopy realizing this structure at the cohomology level. Our algebraic structures are parameterized by props and thus include various kinds of bialgebras. We give a general formula to compute subsets of equivalence classes of realizations as quotients of automorphism groups, and determine the higher homotopy groups via the cohomology of deformation complexes. As a motivating example, we compute subsets of equivalences classes of realizations of Poincaré duality for several examples of manifolds.
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Contributor : Sinan Yalin Connect in order to contact the contributor
Submitted on : Wednesday, February 21, 2018 - 1:06:02 PM
Last modification on : Wednesday, November 3, 2021 - 6:05:19 AM
Long-term archiving on: : Tuesday, May 22, 2018 - 1:53:22 PM


Realization spaces of algebrai...
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  • HAL Id : hal-01714208, version 1



Sinan yalin. Realization spaces of algebraic structures on cochains. International Mathematics Research Notices, Oxford University Press (OUP), 2018, 2018 (1), pp.236-291. ⟨hal-01714208⟩



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