Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling
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.
Keywords
Cite
@article{arxiv.1407.7827,
title = {Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling},
author = {Nathan M. Dunfield and Neil R. Hoffman and Joan E. Licata},
journal= {arXiv preprint arXiv:1407.7827},
year = {2018}
}
Comments
19 pages, 2 figures. v2: minor changes to intro. v3: accepted version, to appear in Math. Res. Letters