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String topology and the based loop space

著者: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve Kerckhoff所有著者
出版商: 2010.
论文: Ph. D. Stanford University 2010
版本/格式:   硕士/博士论文 : 文献 : 硕士论文/博士论文 : 电子图书   计算机文档 : 英语
数据库:WorldCat
提要:
We relate the Batalin-Vilkovisky (BV) algebra structure of the string topology of a manifold to the homological algebra of the singular chains of the based loop space of that manifold, showing that its Hochschild cohomology carries a BV algebra structure isomorphic to that of string topology. Furthermore, this structure is compatible with the usual cup product and Lie bracket on Hochschild cohomology. This  再读一些...
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材料类型: 文献, 硕士论文/博士论文, 互联网资源
文件类型: 互联网资源, 计算机文档
所有的著者/提供者: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
OCLC号码: 665049539
注意: Submitted to the Department of Mathematics.
描述: 1 online resource
责任: Eric James Malm.

摘要:

We relate the Batalin-Vilkovisky (BV) algebra structure of the string topology of a manifold to the homological algebra of the singular chains of the based loop space of that manifold, showing that its Hochschild cohomology carries a BV algebra structure isomorphic to that of string topology. Furthermore, this structure is compatible with the usual cup product and Lie bracket on Hochschild cohomology. This isomorphism arises from a derived form of Poincare duality using modules over the based loop space as local coefficient systems. This derived Poincare duality also comes from a form of fibrewise Atiyah duality on the level of fibrewise spectra, and we use this perspective to connect the algebraic constructions to the Chas-Sullivan loop product.

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