Pacific Institute for the Mathematical Sciences - PIMS

Left-orderability and Dehn surgery

There is a growing body of work that supports a connection between L-spaces and 3-manifolds with non-left-orderable fundamental group, in fact a Seifert fibred manifold is an L-space if and only if its fundamental group is not left-orderable. In this talk I'll provide evidence for a connection that extends beyond the class of Seifert fibred manifolds, by showing that L-spaces behave similarly to non-left-orderability with respect to the operation of Dehn surgery on a manifold. It is with this goal in mind one is led to define a decayed knot; decayed knots have the property that sufficiently large surgery always yields a manifold with non-left-orderable fundamental group.   Moreover, cables of decayed knots are also decayed, as long as the ratio of the cabling coefficients is chosen to be large enough. I'll show how both of these properties mirror the behaviour of knots which admit L-space surgeries, and outline some questions for future research. This is joint work with Liam Watson.

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