Twisted homology operations
Abstract/Contents
- Abstract
- This thesis develops a theory of operations on the twisted homology of E∞-algebras, generalizing a classical theory developed by J.P. May. First we describe a framework suitable for discussing twisted coefficients, which requires working with E∞-algebras in certain categories of functors. In this context, we define twisted versions of the classical Dyer--Lashof operations, as well as a product. Moreover, we prove that these distinguished operations generate all operations on twisted homology by giving a (non-canonical) explicit basis for the homology of free E∞-algebras in terms of these operations. We also make this statement functorial by proving that the homology of a free E∞-algebra is a free object in an appropriate category of objects equipped with an action of the Dyer--Lashof operations. This theory has applications to the study of E∞-spaces with local coefficients, though these are not discussed in detail here.
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 | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Bernard, Calista Kurtz |
|---|---|
| Degree supervisor | Galatius, Søren, 1976- |
| Degree supervisor | Vakil, Ravi |
| Thesis advisor | Galatius, Søren, 1976- |
| Thesis advisor | Vakil, Ravi |
| Thesis advisor | Cohen, Ralph L, 1952- |
| Degree committee member | Cohen, Ralph L, 1952- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Calista Bernard. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/mg702sx7255 |
Access conditions
- Copyright
- © 2021 by Calista Kurtz Bernard
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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