#### Volume 10, issue 3 (2010)

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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 ${B}_{n}$, we denote by ${T}_{w}$ the corresponding transverse braid in $\left({ℝ}^{3},{\xi }_{rot}\right)$. We exhibit, for any two $g,h\in {B}_{n}$, a “comultiplication” map on link Floer homology $\stackrel{̃}{\Phi }:\stackrel{˜}{\mathit{HFL}}\left(m\left({T}_{hg}\right)\right)\to \stackrel{˜}{\mathit{HFL}}\left(m\left({T}_{g}#{T}_{h}\right)\right)$ which sends $\stackrel{̃}{\theta }\left({T}_{hg}\right)$ to $\stackrel{̃}{\theta }\left({T}_{g}#{T}_{h}\right)$. 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
##### 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