Haddley, Joel A
Symmetries of unimodal singularities and complex hyperbolic reflection groups.
Doctor of Philosophy thesis, University of Liverpool.
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Abstract
In search of discrete complex hyperbolic reflection groups in a singularity context, we consider cyclic symmetries of the 14 exceptional unimodal function singularities. In the 3-variable case, we classify all the symmetries for which the restriction of the intersection form of an invariant Milnor fibre to a character subspace has positive signature 1, and hence the corresponding equivariant monodromy is a reflection subgroup of U(k − 1,1). For such subspaces, we construct distinguished vanishing bases and their Dynkin diagrams. For k = 2, the projectivised hyperbolic monodromy is a triangle group of the Poincaré disk. For k = 3, we identify some of the projectivised monodromy groups within a recently published survey by J. R. Parker.
| Item Type: | Thesis (Doctor of Philosophy) |
|---|---|
| Additional Information: | Date: 2011-06 (completed) |
| Subjects: | ?? QA ?? |
| Divisions: | Faculty of Science and Engineering > School of Physical Sciences > Mathematical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 30 Nov 2011 17:04 |
| Last Modified: | 16 Dec 2022 04:35 |
| DOI: | 10.17638/00003313 |
| Supervisors: |
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| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3313 |
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