A parameterized adams spectral sequence for applied topology
Abstract/Contents
- Abstract
- Given an environment that changes over time, under what conditions can it be navigated? From a prescient AI seeking strategies for Frogger to museum thieves trying to avoid the Night Watch (with The Night Watch safely in tow), this is a present and interesting mathematical question. In topological terms, we are interested in the space of sections of a map of spaces X -> I. More broadly, we are interested in describing and computing good invariants for parameterized spaces, which is to say, spaces X equipped with a map to a base space B. We record a number of invariants for such spaces, in the form of sheaves on the base space B, and discuss how these invariants can help us answer the original problem of navigating a changing space. Our main result is the construction of a Bousfield--Kan spectral sequence to aid in computing the "best" of our invariants, the parameterized homotopy groups of a parameterized space. We reinterpret this as an unstable Adams-type spectral sequence, and then give some computations which, in nice cases, computes the homotopy group of the space of sections of a map.
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 | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Mackey, Wyatt Tyrrell |
|---|---|
| Degree supervisor | Carlsson, G. (Gunnar), 1952- |
| Degree supervisor | Vakil, Ravi |
| Thesis advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Vakil, Ravi |
| Thesis advisor | Manolescu, Ciprian, 1978- |
| Degree committee member | Manolescu, Ciprian, 1978- |
| Associated with | Stanford University, School of Humanities and Sciences |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Wyatt Mackey. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/qp579zt0968 |
Access conditions
- Copyright
- © 2023 by Wyatt Tyrrell Mackey
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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