The asymptotic behaviour of Heegaard genus
| dc.creator | Lackenby, Marc | |
| dc.date | 2002-10-21 | |
| dc.date | 2003-11-26 | |
| dc.date.accessioned | 2026-07-07T04:52:10Z | |
| dc.date.available | 2026-07-07T04:52:10Z | |
| dc.description | Let M be a closed orientable 3-manifold with a negatively curved Riemannian metric. Let {M_i} be a collection of finite regular covers with degree d_i. (1) If the Heegaard genus of M_i grows more slowly than the square root of d_i, then M_i has positive first Betti number for all sufficiently large i. (2) The strong Heegaard genus of M_i cannot grow more slowly than the square root of d_i. (3) If the Heegaard genus of M_i grows more slowly than the fourth root of d_i, then M_i fibres over the circle for all sufficiently large i. These results provide supporting evidence for the Heegaard gradient conjecture and the strong Heegaard gradient conjecture. As a corollary to (3), we give a necessary and sufficient condition for M to be virtually fibred in terms of the Heegaard genus of its finite covers. | |
| dc.description | 14 pages. Final version, including a new expository section. To appear in Mathematical Research Letters | |
| dc.identifier | https://arxiv.org/abs/math/0210316 | |
| dc.identifier | http://arxiv.org/abs/math/0210316 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65370 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10; 57M10 | |
| dc.title | The asymptotic behaviour of Heegaard genus | |
| dc.type | text |