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arXiv · 1407.7827

Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling

Nathan M. Dunfield·Neil R. Hoffman·Joan E. Licata
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Abstract

An L-space is a rational homology 3-sphere with minimal Heegaard Floer homology. We give the first examples of hyperbolic L-spaces with no symmetries. In particular, unlike all previously known L-spaces, these manifolds are not double branched covers of links in S^3. We prove the existence of infinitely many such examples (in several distinct families) using a mix of hyperbolic geometry, Floer theory, and verified computer calculations. Of independent interest is our technique for using interval arithmetic to certify symmetry groups and non-existence of isometries of cusped hyperbolic 3-manifolds. In the process, we give examples of 1-cusped hyperbolic 3-manifolds of Heegaard genus 3 with two distinct lens space fillings. These are the first examples where multiple Dehn fillings drop the Heegaard genus by more than one, which answers a question of Gordon.

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Nathan M. Dunfield, Neil R. Hoffman, Joan E. Licata. 2015-06-18. Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling. https://doi.org/10.4310/mrl.2015.v22.n6.a7

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