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String topology and the based loop space

著者: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve Kerckhoffすべての著者
出版: 2010.
論文: Thesis (Ph. D.)--Stanford University, 2010.
エディション/フォーマット:   学位論文/卒業論文 : Document : Thesis/dissertation : 電子書籍   コンピューターファイル : English
データベース:WorldCat
概要:
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  続きを読む
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資料の種類: Document, Thesis/dissertation, インターネット資料
ドキュメントの種類: インターネットリソース, コンピューターファイル
すべての著者/寄与者: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
OCLC No.: 665049539
注記: Submitted to the Department of Mathematics.
物理形態: 1 online resource.
責任者: Eric James Malm.

概要:

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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