Thesis
On surgery presentations of bordism bicategories
- Abstract:
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The d-dimensional bordism (2, 1)-category has as objects closed (d−1)- dimensional manifolds, as 1-morphisms d-dimensional cobordisms, and as 2-morphisms isotopy classes of diffeomorphisms.
In Part I of this thesis, we obtain generators-and-relations presentations of the oriented and unoriented d-dimensional bordism (2, 1)-categories. These presentations, denoted Suror (d−1; d; ∼) and Sur(d−1; d; ∼) respectively, consist of Morse and Cerf graphics suitably decorated with surgery data.
In Part II, we discuss what it means for a 2-categorical presentation to be skeletal. We introduce a general skeletalization procedure and apply it to Suror (1; 2; ∼) . This yields a skeletal presentation of the oriented 2- dimensional bordism (2, 1)-category, which is, in particular, finite.
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- Files:
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(Preview, Dissemination version, pdf, 91.1MB, Terms of use)
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Authors
Contributors
+ Douglas, C
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Mathematical Institute
- Role:
- Supervisor
- ORCID:
- 0000-0003-3146-9314
+ Bartlett, B
- Role:
- Supervisor
+ Tillmann, U
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Mathematical Institute
- Role:
- Supervisor
- ORCID:
- 0000-0002-8076-7660
+ Engineering and Physical Sciences Research Council
More from this funder
- Funder identifier:
- https://ror.org/0439y7842
- Grant:
- 2433258
- DOI:
- Type of award:
- DPhil
- Level of award:
- Doctoral
- Awarding institution:
- University of Oxford
- Language:
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English
- Keywords:
- Subjects:
- Deposit date:
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2026-03-31
- ARK identifier:
Terms of use
- Copyright holder:
- Filippos Ilarion Sytilidis
- Copyright date:
- 2025
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