L-spaces and left-orderability

Liam Watson, UCLA
Fine Hall 314

Various families of examples suggest an interesting correspondence between L-spaces and 3-manifolds with non-left-orderable fundamental group. This motivates the study of left-orderability in the context of Dehn surgery. In particular, since every knot group is left-orderable, we study the phenomenon of when a left-order descends to the quotient group associated with the surgery. This leads to the notion of a decayed knot; such knots have the property that all sufficiently large surgeries have non-left-orderable fundamental group. It can also be shown that sufficiently positive cables of decayed knots are decayed knots. Both of these properties mirror the behaviour of L-spaces under Dehn surgery. This is joint work with Adam Clay.