Factorization theory of Thom spectra, twists, and duality
Abstract/Contents
- Abstract
- This thesis includes two related projects. The first project determines the factorization homology of Thom spectra of n-fold loop maps, and uses this to study the topological Hochschild cohomology of such Thom spectra. Our description of the factorization homology of Thom spectra can be viewed as a twisted form of the non-abelian Poincare duality theorem of Segal, Salvatore, and Lurie, and permits calculations of factorization homology of cobordism spectra and certain Eilenberg-MacLane spectra. Our description of the Hochschild cohomology of these Thom spectra enables calculations and a description in terms of sections of a parametrized spectrum. This allows us to deduce a duality between topological Hochschild homology and topological Hochschild cohomology, and gives ring structures on a certain family of Thom spectra, which were not previously known to be ring spectra. The second project is joint work with Ralph Cohen in which we import the theory of ``Calabi-Yau" algebras and categories from symplectic topology and topological field theories to the setting of spectra. We define two types of Calabi-Yau structures in the setting of ring spectra: one that applies to compact algebras and one that applies to smooth algebras. We apply this theory to describe, prove, and explain a duality between the manifold string topology of Chas and Sullivan and the Lie group string topology of Chataur-Menichi. Using results from the first project in this thesis, we prove that Thom ring spectra of (virtual) bundles over the loop space of a manifold have a Calabi-Yau structure. In the case when the manifold is a sphere, we use this structure to study Lagrangian immersions of the sphere into its cotangent bundle, recasting work of Abouzaid and Kragh.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Klang, Inbar |
|---|---|
| Degree supervisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Galatius, Søren, 1976- |
| Degree committee member | Carlsson, G. (Gunnar), 1952- |
| Degree committee member | Galatius, Søren, 1976- |
| Associated with | Stanford University, Department of Mathematics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Inbar Klang. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Inbar Klang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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