Use this URL to cite or link to this record in EThOS:  http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636868 
Title:  Connectivity of Hurwitz spaces for L₂(7), L₂(11) and S₄  
Author:  Firkin, Adam 
ISNI:
0000 0004 5359 5634


Awarding Body:  University of Birmingham  
Current Institution:  University of Birmingham  
Date of Award:  2015  
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Abstract:  
For a finite group G and collection of conjugacy classes C = (\(C\)\(_1\),…,\(C\)\(_r\)). The (inner) Hurwitz space, H\(^i\)\(^n\)(\(G\), C), is the space of Galois covers of the Riemann sphere with monodromy group isomorphic to \(G\) and ramification type C. Such a space may be parameterized point wise by tuples, g = (\(g\)\(_1\),…,\(g\)\(_r\)) of \(G\), known as Nielsen tuples, such that \(g\)\(_1\)…\(g\)\(_r\) = 1 and \(\langle\)\(g\)\(_1\),…,\(g\)\(_r\)\(\rangle\) generate \(G\). The action of the braid group upon these Nielsen tuples is in a onetoone correspondence with the connected components of Hurwitz spaces. The aim of this thesis is to calculate the connected components of the Hurwitz space for the groups \(L\)\(_2\)(7), \(L\)\(_2\)(11) and \(S\)\(_4\) for any given type in the case of \(L\)\(_2\)(\(p\)) and a particular class of types for \(S\)\(_4\), using the method described. Furthermore, we establish that if two orbits exist we can distinguish these orbits via a lift invariant within the covering group \(SL\)\(_2\)(7) and \(SL\)\(_2\)(11) for \(L\)\(_2\)(7) and \(L\)\(_2\)(11) respectively, and any Schur cover for \(S\)\(_4\).


Supervisor:  Not available  Sponsor:  Engineering and Physical Sciences Research Council (EPSRC)  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.636868  DOI:  Not available  
Keywords:  QA Mathematics  
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