Comultiplication in link Floer homology and transversely nonsimple links

Baldwin, John A

doi:10.2140/agt.2010.10.1417

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Comultiplication in link Floer homology and transversely nonsimple links

John A Baldwin

Algebraic & Geometric Topology 10 (2010) 1417–1436

DOI: 10.2140/agt.2010.10.1417

Abstract

For a word $w$ in the braid group $B_{n}$ , we denote by $T_{w}$ the corresponding transverse braid in $(ℝ^{3}, ξ_{rot})$ . We exhibit, for any two $g, h \in B_{n}$ , a “comultiplication” map on link Floer homology $\tilde{Φ} : \tilde{HFL} (m (T_{h g})) \to \tilde{HFL} (m (T_{g} # T_{h}))$ which sends $\tilde{θ} (T_{h g})$ to $\tilde{θ} (T_{g} # T_{h})$ . 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

Volume 10, issue 3 (2010)