2024/10/07 by Min, Hyunki, Varvarezos, Konstantinos · 2 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2410.05511
In this paper, we define contact invariants in bordered sutured Floer homology. Given a contact 3-manifold with convex boundary, we apply a result of Zarev (arxiv:1010.3496) to derive contact invariants in the bordered sutured modules \widehatBSA and \widehatBSD, as well as in bimodules \widehatBSAA, \widehatBSDD, \widehatBSDA in the case of two boundary components. In the connected boundary case, our invariants appear to agree with bordered contact invariants defined by Alishahi-Földvári-Hendricks-Licata-Petkova-Vértesi (arxiv:2011.08672) whenever the latter are defined, although ours can be defined in broader contexts. We prove that these invariants satisfy a pairing theorem, which is a bordered extension of the Honda-Kazez-Matić gluing map (arxiv:0705.2828) for sutured Floer homology. We also show that there is a correspondence between certain A∞ operations in bordered type-A modules and bypass attachment maps in sutured Floer homology. As an application, we characterize the Stipsicz-Vértesi map from SFH to \widehatHFK as an A∞ action on \widehatCFA. We also apply the immersed curve interpretation of Hanselman-Rasmussen-Watson (arxiv:1604.03466) to prove results involving contact surgery.