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String topology and the based loop space

저자: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve Kerckhoff모든 저자
출판사: 2010.
논문: Ph. D. Stanford University 2010
판/형식:   주제/주장 : 문서 : 눈문/학위논문 : 전자도서   컴퓨터 파일 : 영어
데이터베이스:WorldCat
요약:
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  더 읽기…
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자료 유형: 문서, 눈문/학위논문, 인터넷 자료
문서 형식: 인터넷 자원, 컴퓨터 파일
모든 저자 / 참여자: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
OCLC 번호: 665049539
메모: Submitted to the Department of Mathematics.
설명: 1 online resource
책임: Eric James Malm.

초록:

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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