Souza Roso, Bruno Ricieri;
(2023)
Seiberg-Witten Floer Spectra and Contact Structures.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
In this thesis, the author defines an invariant of rational homology 3-spheres equipped with a contact structure as an element of a cohomotopy set of the Seiberg-Witten Floer spectrum as defined in Manolescu (2003). Furthermore, in light of the equivalence established in Lidman & Manolescu (2018a) between the Borel equivariant homology of said spectrum and the Seiberg-Witten Floer homology of Kronheimer & Mrowka (2007), the author shall show that this homotopy theoretic invariant recovers the already well known contact element in the Seiberg-Witten Floer cohomology (vid. e.g. Kronheimer, Mrowka, Ozsváth & Szabó 2007) in a natural fashion. Next, the behaviour of the cohomotopical invariant is considered in the presence of a finite covering. This setting naturally asks for the use of Borel cohomology equivariant with respect to the group of deck transformations. Hence, a new equivariant contact invariant is defined and its properties studied. The invariant is then computed in one concrete example, wherein the author demonstrates that it opens the possibility of considering scenarios hitherto inaccessible.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Seiberg-Witten Floer Spectra and Contact Structures |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10165679 |
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