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Title: Symmetries of unimodal singularities and complex hyperbolic reflection groups
Author: Haddley, Joel A.
ISNI:       0000 0004 2706 7299
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2011
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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.
Supervisor: Goryunov, Victor V. ; Pratoussevitch, Anna Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: QA Mathematics