Knot Floer homology in cyclic branched covers
| dc.creator | Grigsby, J Elisenda | |
| dc.date | 2005-07-25 | |
| dc.date | 2009-04-23 | |
| dc.date.accessioned | 2026-07-07T13:07:22Z | |
| dc.date.available | 2026-07-07T13:07:22Z | |
| dc.description | In this paper, we introduce a sequence of invariants of a knot K in S^3: the knot Floer homology groups of the preimage of K in the m-fold cyclic branched cover over K. We exhibit the knot Floer homology in the m-fold branched cover as the categorification of a multiple of the Turaev torsion in the case where the m-fold branched cover is a rational homology sphere. In addition, when K is a 2-bridge knot, we prove that the knot Floer homology of the lifted knot in a particular Spin^c structure in the branched double cover matches the knot Floer homology of the original knot K in S^3. We conclude with a calculation involving two knots with identical knot Floer homology in S^3 for which the knot Floer homology groups in the double branched cover differ as Z_2-graded groups. | |
| dc.description | This is the version published by Algebraic & Geometric Topology on 25 September 2006 | |
| dc.identifier | https://arxiv.org/abs/math/0507498 | |
| dc.identifier | http://arxiv.org/abs/math/0507498 | |
| dc.identifier | Algebr. Geom. Topol. 6 (2006) 1355-1398 | |
| dc.identifier | doi:10.2140/agt.2006.6.1355 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228070 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27, 57R58, 57M05 | |
| dc.title | Knot Floer homology in cyclic branched covers | |
| dc.type | text |