Left-Orderable Groups and Dehn Surgery
Left-Orderable Groups and Dehn Surgery
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Konstantinos Varvarezos, Princeton University
A left-ordering on a group is a way of ordering its elements听which is compatible with the group multiplication.听Such orderings are of interest in topology in part due to connections with foliations and听 Heegaard Floer homology - in particular, there is an outstanding conjecture relating taut foliations, L-spaces, and left-orderable fundamental groups of rational homology 3-spheres. We discuss the special case of manifolds obtained by Dehn surgery on a knot and investigate a technique for constructing left-orderings for such manifolds.
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