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Symmetries of unimodal singularities and complex hyperbolic reflection groups

Haddley, Joel A. (2011) Symmetries of unimodal singularities and complex hyperbolic reflection groups. Doctoral thesis, University of Liverpool.

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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 (Doctoral)
Subjects:Q Science > QA Mathematics
Departments, Research Centres and Related Units:Academic Faculties, Institutes and Research Centres > Faculty of Science > Department of Mathematical Sciences
ID Code:3313
Deposited On:30 Nov 2011 17:04
Last Modified:24 Apr 2012 10:51

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