Day, Lucas;
(2025)
Poincaré Complexes and Exotic
Manifolds with Finite Fundamental Groups.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
The first part of this thesis investigates the classification of (n-1)-connected 2n-dimensional Poincaré complexes, with a focus on their homotopy properties and connections to closed smooth manifolds. The second part explores applications to non-simply connected Poincaré complexes. By constructing free actions of finite groups on certain non-smoothable, highly connected Poincaré complexes, we establish a foundation for further studies in surgery theory. Finally, the thesis examines exotic spheres and their use in constructing PL-manifolds with different, diffeomorphically distinct, smooth structures. Key results include free actions of finite groups on non-standard smoothings of highly connected PL-manifolds. In particular, the results highlight that there is a necessary distinction to be made between a PL-homeomorphism and a diffeomorphism when considering the classification of certain non-simply connected manifolds with highly-connected universal covering spaces.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Poincaré Complexes and Exotic Manifolds with Finite Fundamental Groups |
| Language: | English |
| Additional information: | Copyright © The Author 2025. 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/10213415 |
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