A homotopy-theoretic view of Bott-Taubes integrals and knot spaces
Abstract/Contents
- Abstract
- We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber'' classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is essentially the one considered by Bott and Taubes, who integrated differential forms along the fiber to get knot invariants. By doing this "integration'' homotopy-theoretically, we are able to produce integral cohomology classes. Inspired by results of Budney and Cohen, we study how this integration is compatible with homology operations on the space of long knots. In particular we derive a product formula for evaluations of cohomology classes on homology classes, with respect to connect-sum of knots. We then adapt the construction to be compatible with tools coming from the Goodwillie-Weiss embedding calculus, in particular Sinha's cosimplicial model for the space of knots.
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 | Koytcheff, Robin Michael John |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Galatius, Søren, 1976- |
| Thesis advisor | Ionel, Eleny |
| Advisor | Galatius, Søren, 1976- |
| Advisor | Ionel, Eleny |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Robin Koytcheff. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph. D.)--Stanford University, 2010. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2010 by Robin Michael John Koytcheff
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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