Lspaces and leftorderability
Lspaces and leftorderability

Liam Watson, UCLA
Fine Hall 314
Various families of examples suggest an interesting correspondence between Lspaces and 3manifolds with nonleftorderable fundamental group. This motivates the study of leftorderability in the context of Dehn surgery. In particular, since every knot group is leftorderable, we study the phenomenon of when a leftorder 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 nonleftorderable 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 Lspaces under Dehn surgery. This is joint work with Adam Clay.