Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling
| Autor: | Neil R. Hoffman, Joan E. Licata, Nathan M. Dunfield |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Popis: | 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. 19 pages, 2 figures. v2: minor changes to intro. v3: accepted version, to appear in Math. Res. Letters |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|