Realization Spaces of Algebraic Structures on Cochains
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Realization Spaces of Algebraic Structures on Cochains. / Yalin, Sinan.
I: International Mathematics Research Notices, Bind 2018, Nr. 1, 01.2018, s. 236-291.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Realization Spaces of Algebraic Structures on Cochains
AU - Yalin, Sinan
PY - 2018/1
Y1 - 2018/1
N2 - 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.
AB - 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.
U2 - 10.1093/imrn/rnw239
DO - 10.1093/imrn/rnw239
M3 - Journal article
VL - 2018
SP - 236
EP - 291
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 1
ER -
ID: 202283931