Symmetries of unimodal singularities and complex hyperbolic reflection groups

Haddley, Joel A ORCID: 0000-0003-2947-6718 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:	08 Feb 2025 00:07
DOI:	10.17638/00003313
Supervisors:	Goryunov, Victor V Pratoussevitch, Anna
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3313