[en] Given an algebraic structure on the homology of a chain complex, we define its realization space as a Kan complex whose vertices are the structures up to homotopy realizing this structure at the homology level. Our algebraic structures are parametrised by props and thus include various kinds of bialgebras. We give a general formula to compute subsets of equivalences 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 Poincar\'e duality for several examples of manifolds.
Disciplines :
Mathematics
Author, co-author :
Yalin, Sinan ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Realization spaces of algebraic structures on chains