Realization spaces of algebraic structures on cochains - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Mathematics Research Notices Année : 2018

Realization spaces of algebraic structures on cochains

Sinan Yalin

Résumé

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.
Fichier principal
Vignette du fichier
Realization spaces of algebraic structures on cochains.pdf (529.3 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01714208 , version 1 (21-02-2018)

Identifiants

  • HAL Id : hal-01714208 , version 1

Citer

Sinan Yalin. Realization spaces of algebraic structures on cochains. International Mathematics Research Notices, 2018, 2018 (1), pp.236-291. ⟨hal-01714208⟩
102 Consultations
86 Téléchargements

Partager

Gmail Facebook X LinkedIn More