Geodesic
Knots which admit a surgery with simple knot Floer homology groups
Eftekhary, Eaman1
1School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran 19395, Iran
Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1243-1256
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We show that if a positive integral surgery on a knot K inside a homology sphere X results in an induced knot Kn ⊂ Xn(K) = Y which has simple Floer homology then n ≥ 2g(K). Moreover, for X = S3 the three-manifold Y is an L–space, and the Heegaard Floer homology groups of K are determined by its Alexander polynomial.

DOI : 10.2140/agt.2011.11.1243
Keywords: simple knot Floer homology, L–space surgery

Eftekhary, Eaman  1

1 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran 19395, Iran 
@article{10_2140_agt_2011_11_1243,
     author = {Eftekhary, Eaman},
     title = {Knots which admit a surgery with simple knot {Floer} homology groups},
     journal = {Algebraic and Geometric Topology},
     pages = {1243--1256},
     year = {2011},
     volume = {11},
     number = {3},
     doi = {10.2140/agt.2011.11.1243},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.1243/}
}
TY  - JOUR
AU  - Eftekhary, Eaman
TI  - Knots which admit a surgery with simple knot Floer homology groups
JO  - Algebraic and Geometric Topology
PY  - 2011
SP  - 1243
EP  - 1256
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.1243/
DO  - 10.2140/agt.2011.11.1243
ID  - 10_2140_agt_2011_11_1243
ER  - 
%0 Journal Article
%A Eftekhary, Eaman
%T Knots which admit a surgery with simple knot Floer homology groups
%J Algebraic and Geometric Topology
%D 2011
%P 1243-1256
%V 11
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.1243/
%R 10.2140/agt.2011.11.1243
%F 10_2140_agt_2011_11_1243
Eftekhary, Eaman. Knots which admit a surgery with simple knot Floer homology groups. Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1243-1256. doi: 10.2140/agt.2011.11.1243

[1] K L Baker, J E Grigsby, M Hedden, Grid diagrams for lens spaces and combinatorial knot Floer homology, Int. Math. Res. Not. (2008) 39

[2] E Eftekhary, Floer homology and existence of incompressible tori in homology spheres

[3] E Eftekhary, Floer homology and splicing knot complements

[4] E Eftekhary, Knots inside homology spheres with simple knot Floer homology are trivial

[5] E Eftekhary, Longitude Floer homology and the Whitehead double, Algebr. Geom. Topol. 5 (2005) 1389

[6] E Eftekhary, A combinatorial approach to surgery formulas in Heegaard Floer homology, Algebr. Geom. Topol. 9 (2009) 2225

[7] M Hedden, On Floer homology and the Berge conjecture on knots admitting lens space surgeries, Trans. Amer. Math. Soc. 363 (2011) 949

[8] Y Ni, Link Floer homology detects the Thurston norm, Geom. Topol. 13 (2009) 2991

[9] P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311

[10] P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58

[11] P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. $(2)$ 159 (2004) 1027

[12] P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281

[13] P Ozsváth, Z Szabó, Knot Floer homology and integer surgeries, Algebr. Geom. Topol. 8 (2008) 101

[14] J Rasmussen, Lens space surgeries and L–space homology spheres

[15] J Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003)

Cité par Sources :