Comultiplication in link floer homology and transversely nonsimple links

Abstract

For a word w in the braid group Bn, we denote by Tw the corresponding transverse braid in (R3,ξrot). We exhibit, for any two g; h Ie{cyrillic, ukrainian} Bn, a "comultiplication" map on link Floer homology F{cyrillic} HFL (m(Thg)) → HFL (m(Tg#Th)) which sends Θ(Thg) to Θ(Tg#Th) We use this comultiplication map to generate infinitely many new examples of prime topological link types which are not transversely simple.