Sutton, Erin;
(2019)
Algebraic Aspects of Poincaré Duality.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Let G be a finite group. It is an unsolved problem to classify closed connected manifolds with fundamental group G. This thesis represents a first approximation to solving this problem. We consider the universal covers of such manifolds, and require that these covers be connected up to, but not including, the middle dimension, and that they satisfy a specific formulation of Poincaré Duality originally set out by Lefschetz. Using results from homological algebra, in particular the work of Johnson and Remez in constructing diagonal resolutions for metacyclic groups, we are able to construct purely algebraic chain complexes and invariants which act as a first approximation to these universal covers for the cases G cyclic and metacyclic.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Algebraic Aspects of Poincaré Duality |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2019. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices 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-pp.ucl.ac.uk/id/eprint/10067970 |
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