Bounds on the Number of Automorphisms of a Compact Non-orientable Surface of Given Genus

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dc.contributor.author Vasiljevic, Sanja Todorovic en
dc.date.accessioned 2007-07-09T11:42:43Z en
dc.date.available 2007-07-09T11:42:43Z en
dc.date.issued 2001 en
dc.identifier THESIS 01-404 en
dc.identifier.citation Thesis (PhD--Mathematics)--University of Auckland, 2001 en
dc.identifier.uri http://hdl.handle.net/2292/730 en
dc.description Full text is available to authenticated members of The University of Auckland only. en
dc.description.abstract This thesis reports on an investigation of lower bounds on the largest number ν(ρ) of automorphisms of a non-orientable surface of given genus ρ>2. In unpublished work, it has been shown by Conder, Maclachlan and Wilson that ν(ρ)≥ 8(ρ-Z) if ρ is even, and ν(ρ) ≥ 4ρ if. ρ is odd, and that improvements are possible for genera in specific residue classes modulo 3 or 4. The main part of this thesis is devoted to proving that the bounds obtained by Conder, Maclachlan and Wilson are sharp for infinitely many values of ρ in each residue class modulo 12, with the exception of the case ρ ≡ 3 mod 12. In the latter case, some evidence is given in support of the conjecture that the lower bound of ν(ρ) ≥ 4ρ is sharp for infinitely many p of the form 83q where q is a prime congruent to 11 mod 144. In addition, a classification is given of large groups of automorphisms of non-orientable surfaces of small genus. Specifically, all instances are determined of the action of a group of more than 4ρ automorphisms of a non-orientable surface of genus p between 3 and 15 (inclusive). The approach taken to proving sharpness and classifying actions on surfaces of small genus is algebraic, using techniques from group theory and some computer-assisted calculations. en
dc.language.iso en en
dc.publisher ResearchSpace@Auckland en
dc.relation.ispartof PhD Thesis - University of Auckland en
dc.relation.isreferencedby UoA99100341214002091 en
dc.rights Restricted Item. Available to authenticated members of The University of Auckland. en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Bounds on the Number of Automorphisms of a Compact Non-orientable Surface of Given Genus en
dc.type Thesis en
thesis.degree.grantor The University of Auckland en
thesis.degree.level Doctoral en
thesis.degree.name PhD en
dc.rights.holder Copyright: The author en


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