Hollands, Edwin;
(2025)
Knörrer periodicity as a deformation of matrix
factorisation categories.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Knörrer periodicity is an equivalence of matrix factorisations categories which has been proven to hold under certain fairly restrictive conditions. We show that the phenomenon can be understood as a deformation of categories even in the cases where there is no equivalence. The class of this deformation in the Hochschild cohomology of the category can be thought of as a local obstruction to Knörrer periodicity. Furthermore, we study this deformation and show there is a strong argument that if we assume the equivalence to hold and the triviality of the deformation up to first order, then the conditions mentioned above are necessary. This presents an approximate converse to Knörrer periodicity.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Knörrer periodicity as a deformation of matrix factorisation categories |
| Open access status: | An open access version is available from UCL Discovery |
| 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/10213315 |
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