Obstruction theory for operadic algebras
Obstruction theory for operadic algebras
View/Type of Scholarly Publication
DissertationDate of Exam
04.05.2012Date of Publication
21.05.2012Advisor
Schwede, StefanCo-Referee
Richter, BirgitMetadata
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Abstract
We study obstruction theory for formality of chain operadic algebras. We construct a canonical class γA for an algebra A over a cofibrant chain operad P∞. This class takes values in the Gamma cohomology groups of the homology algebra H*A and depends only on the homotopy type of the algebra. If the canonical class vanishes then there is a successive obstruction. Further, we give a criterion for when two P∞ -algebras are of the same homotopy type.
Subjects
Hindernistheorie, Operaden, formale Algebren, E_infinity, A_infinity
Classification (DDC)
510 MathematikDimitrova, Boryana: Obstruction theory for operadic algebras. - Bonn, 2012. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-28395
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-28395
@phdthesis{handle:20.500.11811/5307,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-28395,
author = {{Boryana Dimitrova}},
title = {Obstruction theory for operadic algebras},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = may,
note = {We study obstruction theory for formality of chain operadic algebras. We construct a canonical class γA for an algebra A over a cofibrant chain operad P∞. This class takes values in the Gamma cohomology groups of the homology algebra H*A and depends only on the homotopy type of the algebra. If the canonical class vanishes then there is a successive obstruction. Further, we give a criterion for when two P∞ -algebras are of the same homotopy type.},
url = {https://hdl.handle.net/20.500.11811/5307}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-28395,
author = {{Boryana Dimitrova}},
title = {Obstruction theory for operadic algebras},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = may,
note = {We study obstruction theory for formality of chain operadic algebras. We construct a canonical class γA for an algebra A over a cofibrant chain operad P∞. This class takes values in the Gamma cohomology groups of the homology algebra H*A and depends only on the homotopy type of the algebra. If the canonical class vanishes then there is a successive obstruction. Further, we give a criterion for when two P∞ -algebras are of the same homotopy type.},
url = {https://hdl.handle.net/20.500.11811/5307}
}
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