Comultiplication in link Floer homology and transversely non-simple links
arXiv:0910.1102 · doi:10.2140/agt.2010.10.1417
Abstract
For a word w in the braid group on n-strands, we denote by T_w the corresponding transverse braid in the rotational symmetric tight contact structure on S^3. We exhibit a map on link Floer homology which sends the transverse invariant associated to T_{ws_i} to that associated to T_w, where s_i is one of the standard generators of B_n. This gives rise to a "comultiplication" map on link Floer homology. We use this to generate infinitely many new examples of prime topological link types which are not transversely simple.
16 pages, 10 figures