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Some bounds for the knot Floer $\tau$–invariant of satellite knots

Lawrence P Roberts
Algebraic & Geometric Topology 12 (2012) 449–467
DOI: 10.2140/agt.2012.12.449
Abstract

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.

Keywords
$\tau$–invariant, satellite knots, Heegaard Floer homology
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R58
References
Publication
Received: 31 March 2010
Revised: 24 February 2011
Accepted: 22 November 2011
Published: 20 March 2012
Authors
Lawrence P Roberts
Department of Mathematics
University of Alabama
Box 870350
Tuscaloosa AL 35487-0350
USA
http://www.bama.ua.edu/~lproberts