2019/06/20 by Miller, Maggie
#57N10 #57R30 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1906.08458
Let L be an n-component link (n>1) with pairwise nonzero linking numbers in a rational homology 3-sphere Y. Assume the link complement X:=Y∖ν(L) has nondegenerate Thurston norm. In this paper, we study when a Thurston norm-minimizing surface S properly embedded in X remains norm-minimizing after Dehn filling all boundary components of X according to ∂ S and capping off ∂ S by disks. In particular, for n=2 the capped-off surface is norm-minimizing when [S] lies outside of a finite set of rays in H2(X,∂ X;ℝ). When Y is an integer homology sphere this gives an upper bound on the number of surgeries on L which may yield S1× S2. The main techniques come from Gabai's proof of the Property R conjecture and related work.