Geodesic
Some bounds for the knot Floer τ–invariant of satellite knots
Roberts, Lawrence P1
1Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa AL 35487-0350, USA
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 449-467
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This paper uses four dimensional handlebody theory to compute upper and lower bounds for the Heegaard Floer τ–invariant of almost all satellite knots in terms of the τ–invariants of the pattern and the companion.

DOI : 10.2140/agt.2012.12.449
Keywords: $\tau$–invariant, satellite knots, Heegaard Floer homology

Roberts, Lawrence P  1

1 Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa AL 35487-0350, USA 
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Roberts, Lawrence P. Some bounds for the knot Floer τ–invariant of satellite knots. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 449-467. doi: 10.2140/agt.2012.12.449

[1] M Hedden, Knot Floer homology of Whitehead doubles, Geom. Topol. 11 (2007) 2277

[2] M Hedden, On knot Floer homology and cabling : 2, Int. Math. Res. Not. 2009 (2009) 2248

[3] M Hedden, P Ording, The Ozsváth–Szabó and Rasmussen concordance invariants are not equal, Amer. J. Math. 130 (2008) 441

[4] C Livingston, Computations of the Ozsváth–Szabó knot concordance invariant, Geom. Topol. 8 (2004) 735

[5] C Livingston, S Naik, Ozsváth–Szabó and Rasmussen invariants of doubled knots, Algebr. Geom. Topol. 6 (2006) 651

[6] P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179

[7] P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615

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

[9] P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. 159 (2004) 1159

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

[11] I Petkova, Cables of thin knots and bordered Heegaard Floer homology

[12] L Roberts, Extending Van Cott’s bounds for the τ and s–invariants of a satellite knot, J. Knot Theory Ramifications 20 (2011) 1237

[13] C A Van Cott, Ozsváth–Szabó and Rasmussen invariants of cable knots, Algebr. Geom. Topol. 10 (2010) 825

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