Asymmetric L-space knots

2017/10/04 by Kenneth L. Baker, John Luecke · 1 citation
Mathematics · #math.GT #msc:57M25 #msc:57M27

paper · pdf · doi:10.2140/gt.2020.24.2287

published as Geom. Topol. 24 (2020) 2287-2359

arxiv created 2017/10/04 · arxiv updated 2021/01/06

Abstract

We construct the first examples of asymmetric L-space knots in S³. More specifically, we exhibit a construction of hyperbolic knots in S³ with both (i) a surgery that may be realized as a surgery on a strongly invertible link such that the result of the surgery is the double branched cover of an alternating link and (ii) trivial isometry group. In particular, this produces L-space knots in S³ which are not strongly invertible. The construction also immediately extends to produce asymmetric L-space knots in any lens space, including S¹ × S².

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