String topology and the based loop space
Abstract/Contents
- Abstract
- 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.
Description
Type of resource | text |
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Form | electronic; electronic resource; remote |
Extent | 1 online resource. |
Publication date | 2010 |
Issuance | monographic |
Language | English |
Creators/Contributors
Associated with | Malm, Eric James | |
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Associated with | Stanford University, Department of Mathematics | |
Primary advisor | Cohen, Ralph L, 1952- | |
Thesis advisor | Cohen, Ralph L, 1952- | |
Thesis advisor | Carlsson, G. (Gunnar), 1952- | |
Thesis advisor | Galatius, Søren, 1976- | |
Thesis advisor | Kerckhoff, Steve | |
Advisor | Carlsson, G. (Gunnar), 1952- | |
Advisor | Galatius, Søren, 1976- | |
Advisor | Kerckhoff, Steve |
Subjects
Genre | Theses |
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Bibliographic information
Statement of responsibility | Eric James Malm. |
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Note | Submitted to the Department of Mathematics. |
Thesis | Thesis (Ph.D.)--Stanford University, 2010. |
Location | electronic resource |
Access conditions
- Copyright
- © 2010 by Eric James Malm
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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