Mohammed Salih, Haval M. (2015). Finite groups of small genus. University of Birmingham. Ph.D.
|
MohammedSalih15PhD.pdf
PDF - Accepted Version Download (1MB) |
Abstract
For a finite group \(G\), the Hurwitz space \(H\)\(^i\)\(_r\)\(_,\)\(^n\)\(_g\) (\(G\)) is the space of genus \(g\) covers of the Riemann sphere with \(r\) branch points and the monodromy group \(G\). Let ε\(_r\)(\(G\)) = {(\(x\)\(_1\),...,\(x\)\(_r\)) : \(G\) = \(\langle\)\(x\)\(_1\),...,\(x\)\(_r\)\(\rangle\), Π\(^r\)\(_i\)\(_=\)\(_1\) \(x\)\(_i\) = 1, \(x\)\(_i\) ϵ \(G\)#, \(i\) = 1,...,\(r\)}. The connected components of \(H\)\(^i\)\(_r\)\(_,\)\(^n\)\(_g\)(\(G\)) are in bijection with braid orbits on ε\(_r\)(\(G\)).
In this thesis we enumerate the connected components of \(H\)\(^i\)\(_r\)\(_,\)\(^n\)\(_g\)(\(G\)) in the cases where \(g\) \(\leq\) 2 and \(G\) is a primitive affine group. Our approach uses a combination of theoretical and computational tools. To handle the most computationally challenging cases we develop a new algorithm which we call the Projection-Fiber algorithm.
Type of Work: | Thesis (Doctorates > Ph.D.) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Award Type: | Doctorates > Ph.D. | |||||||||
Supervisor(s): |
|
|||||||||
Licence: | ||||||||||
College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | |||||||||
School or Department: | School of Mathematics | |||||||||
Funders: | None/not applicable | |||||||||
Subjects: | Q Science > QA Mathematics | |||||||||
URI: | http://etheses.bham.ac.uk/id/eprint/5574 |
Actions
Request a Correction | |
View Item |
Downloads
Downloads per month over past year