Realization Spaces of Algebraic Structures on Cochains

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Realization Spaces of Algebraic Structures on Cochains. / Yalin, Sinan.

In: International Mathematics Research Notices, Vol. 2018, No. 1, 01.2018, p. 236-291.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Yalin, S 2018, 'Realization Spaces of Algebraic Structures on Cochains', International Mathematics Research Notices, vol. 2018, no. 1, pp. 236-291. https://doi.org/10.1093/imrn/rnw239

APA

Yalin, S. (2018). Realization Spaces of Algebraic Structures on Cochains. International Mathematics Research Notices, 2018(1), 236-291. https://doi.org/10.1093/imrn/rnw239

Vancouver

Yalin S. Realization Spaces of Algebraic Structures on Cochains. International Mathematics Research Notices. 2018 Jan;2018(1):236-291. https://doi.org/10.1093/imrn/rnw239

Author

Yalin, Sinan. / Realization Spaces of Algebraic Structures on Cochains. In: International Mathematics Research Notices. 2018 ; Vol. 2018, No. 1. pp. 236-291.

Bibtex

@article{6afcd4d6f1f342bf8d5ccd6b6484cc3a,
title = "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 Poincar{\'e} duality for several examples of manifolds.",
author = "Sinan Yalin",
year = "2018",
month = jan,
doi = "10.1093/imrn/rnw239",
language = "English",
volume = "2018",
pages = "236--291",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "1",

}

RIS

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