Volume 10, issue 3 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Comultiplication in link Floer homology and transversely nonsimple links

John A Baldwin

Algebraic & Geometric Topology 10 (2010) 1417–1436
Abstract

For a word w in the braid group Bn, we denote by Tw the corresponding transverse braid in (3,ξrot). We exhibit, for any two g,h Bn, a “comultiplication” map on link Floer homology Φ̃: HFL˜(m(Thg)) HFL˜(m(Tg#Th)) which sends θ̃(Thg) to θ̃(Tg#Th). We use this comultiplication map to generate infinitely many new examples of prime topological link types which are not transversely simple.

Keywords
knot, link, transverse, knot Floer homology, contact structure, Heegaard Floer
Mathematical Subject Classification 2000
Primary: 57M27, 57R17
References
Publication
Received: 19 October 2009
Revised: 16 February 2010
Accepted: 21 February 2010
Published: 25 June 2010
Authors
John A Baldwin
Department of Mathematics
Princeton University
Princeton, NJ 08544-1000
http://www.math.princeton.edu/~baldwinj