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String topology and the based loop space

作者: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve Kerckhoff所有作者
出版商: 2010.
論文: Thesis (Ph. D.)--Stanford University, 2010.
版本/格式:   碩士/博士論文 : 文獻 : 碩士論文/博士論文 : 電子書   電腦資料 : 英語
資料庫: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  再讀一些...
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資料類型: 文獻, 碩士論文/博士論文, 網際網路資源
文件類型: 網路資源, 電腦資料
所有的作者/貢獻者: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
OCLC系統控制編碼: 665049539
注意: Submitted to the Department of Mathematics.
描述: 1 online resource.
責任: 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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