# Constructions of asymmetric L-space knots

Presented by:
Ken Baker University of Miami
Date:
Wednesday 1st February 2017 - 10:00 to 11:00
Venue:
INI Seminar Room 1
Abstract:

Until July 2014, all known L-spaces admitted an involution.  Then, through a clever search of the SnapPy census, Dunfield-Hoffman-Licata found examples of asymmetric one-cusped hyperbolic manifolds with two lens space fillings and consequently many asymmetric L-space fillings. Yet since none of these lens space fillings were $S^3$, so still stood the conjecture that L-space knots in $S^3$ are strongly invertible.

In this talk we present
(1) a `natural' realization and vast generalization of the Dunfield-Hoffman-Licata examples (joint work with Hoffman and Licata) and
(2) the first construction of asymmetric L-space knots in $S^3$ (joint work with Luecke).

Both of these constructions produce asymmetric one-cusped hyperbolic manifolds with two fillings that are double branched covers of alternating links, though the approaches are different.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Presentation Material: