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

Nathan M. Dunfield, Neil R. Hoffman, Joan E. Licata

Research output: Contribution to journalArticle

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 S3. 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.

Original languageEnglish (US)
Pages (from-to)1679-1698
Number of pages20
JournalMathematical Research Letters
Volume22
Issue number6
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Mathematics(all)

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