Haddley, Joel A
Symmetries of unimodal singularities and complex hyperbolic reflection groups.
[Unspecified]
![]() |
PDF
Thesis_-_Joel_Haddley.pdf - Submitted Version Access to this file is embargoed until Unspecified. Available under License Creative Commons Attribution No Derivatives. Download (789kB) |
![]() |
PDF (Renamed version)
HaddleyJoe_Jun2011_3313.pdf - Accepted Version Available under License Creative Commons Attribution No Derivatives. Download (789kB) |
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: | Unspecified |
---|---|
Additional Information: | Date: 2011-06 (completed) |
Subjects: | Q Science > QA Mathematics |
Divisions: | ?? dep_math ?? |
Depositing User: | Symplectic Admin |
Date Deposited: | 30 Nov 2011 17:04 |
Last Modified: | 09 Jan 2021 08:57 |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3313 |