2022/02/25 by Kang, Sungkyung
#57R58 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57K18 #Secondary 57K31
paper · doi:10.48550/arxiv.2202.12500
We prove that, up to local equivalences, a suitable truncation of the involutive knot Floer homology of a knot in S3 and the involutive bordered Heegaard Floer theory of its complement determine each other. In particular, given two knots K1 and K2, we prove that the \mathbbF2[U,V]/(UV)-coefficient involutive knot Floer homology of K1 \sharp -K2 is ιK-locally trivial if \widehatCFD(S3 \backslash K1) and \widehatCFD(S2 \backslash K2) satisfy a certain condition which can be seen as the bordered counterpart of ιK-local equivalence. We further establish an explicit algebraic formula that computes the hat-flavored truncation of the involutive knot Floer homology of a knot from the involutive bordered Floer homology of its complement. It follows that there exists an algebraic satellite operator defined on the local equivalence group of knot Floer chain complexes, which can be computed explicitly up to a suitable truncation.