McInroy, Justin Fergus (2011)
Ph.D. thesis, University of Birmingham.
| AbstractLet \(\Pi\) 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.
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