Title: Homotopy groups of manifolds
Lead Research Organisation:
University of Southampton
Department Name: Sch of Mathematical Sciences
Abstract
Manifolds are fundamental objects in geometry and physics.
The study of their algebraic topology has a long and rich history. However,
until recently there have been no systematic tools to study their homotopy
groups. Work of Beben and Theriault developed new methods for looking
deeper into the homotopy theory of manifolds by decomposing their based
loop spaces into a product of more recognisable factors, and this was applied
to determine the homotopy groups of certain specific families of manifolds.
The aim of the project is to develop the methods and apply them to a wider
range of manifolds.
The study of their algebraic topology has a long and rich history. However,
until recently there have been no systematic tools to study their homotopy
groups. Work of Beben and Theriault developed new methods for looking
deeper into the homotopy theory of manifolds by decomposing their based
loop spaces into a product of more recognisable factors, and this was applied
to determine the homotopy groups of certain specific families of manifolds.
The aim of the project is to develop the methods and apply them to a wider
range of manifolds.
Organisations
People |
ORCID iD |
| Stephen Theriault (Primary Supervisor) | |
| Sebastian Chenery (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R513325/1 | 01/10/2018 | 30/09/2023 | |||
| 2281748 | Studentship | EP/R513325/1 | 01/10/2019 | 30/09/2022 | Sebastian Chenery |
| Description | My PhD is in the subject area of algebraic topology, with a specific focus on the homotopy theory of manifolds. Manifolds are highly geometric objects, fundamental to many areas of mathematics, and I study them from a topological viewpoint using novel techniques that give direct insight into their homotopy groups (a foundational algebraic construction of homotopy theory). My results shed new light on several homotopy theoretic problems, most notably those involving connected sums - these are a natural way that one may attempt to decompose a manifold into its constituent parts, analogous to decomposing an integer into a product of primes. Studying their homotopy theoretic behaviour has profound implications for classification problems, and my work in this area has been accepted for publication by the Proceedings of the Edinburgh Mathematical Society, an influential journal. |
| Exploitation Route | Further work by mathematicians. |
| Sectors | Other |
| URL | https://arxiv.org/abs/2203.11064 |