Realization spaces of algebraic structures on cochains
Abstract
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.
Cite
@article{arxiv.1503.03724,
title = {Realization spaces of algebraic structures on cochains},
author = {Sinan Yalin},
journal= {arXiv preprint arXiv:1503.03724},
year = {2016}
}
Comments
Typo corrections, explanations improved for some technical parts. Correction of a mistake concerning the result about connected components of realization spaces, and another one concerning relative realization spaces. 40 pages, to appear in IMRN