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 |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2010 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Malm, Eric James |
|---|---|
| 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 |
|---|
Bibliographic information
| Statement of responsibility | Eric James Malm. |
|---|---|
| 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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