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### Constructions of asymmetric L-space knots

**Geometry/Topology**

Speaker: | Ken Baker, University of Miami |

Location: | 1147 MSB |

Start time: | Mon, Feb 26 2018, 1:10PM |

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.