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Title: A family of biaffine geometries and their resulting amalgams
Author: McInroy, Justin Fergus
ISNI:       0000 0004 2705 4543
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2011
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Let \(\Pi\) be a thick polar space of rank \(n\) at least three. Pick a hyperplane \(F\) of \(\Pi\) and \(H\) of \(\Pi\)\(^{\ast}\). Define the elements of a biaffine polar space \(\Gamma\) to be those elements of \(\Pi\) which are not contained in \(F\), or dually in \(H\). We show that \(\Gamma\) is a non empty geometry which is simply connected, except for a few small exceptions for \(\Pi\). We give two pairs of examples with ag-transitive groups, which lead to amalgam results for recognising either one of \(q\)\(^6\) : \(SU\)\(_3\)\((q)\) or \(G\)\(_2\)\((q)\), or one of \(q\)\(^7\) : \(G\)\(_2\)\((q)\) or \(Spin\)\(^7\)\((q)\). Also, we give details of a computer program to calculate the fundamental group of a given geometry.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics