Simple Connectivity in Polar Spaces with Group-Theoretic Applications
Nessler, Reed, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Abramenko, Peter, Department of Mathematics, University of Virginia
In this dissertation, I prove that ∆°( C ) is simply connected, for any chamber C of a nonembeddable polar space ∆, using a recent coordinate description of these spaces. This fact is used in describing some group amalgamations in the setting of BN-pairs and related structures. Finally I discuss some progress in studying ∆°( C ) in a building of type F4.
PHD (Doctor of Philosophy)
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