A family of biaffine geometries and their resulting amalgams

McInroy, Justin Fergus (2011). A family of biaffine geometries and their resulting amalgams. University of Birmingham. Ph.D.

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Abstract

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.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Shpectorov, SergeyUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/1626

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