The effect of link Dehn surgery on the Thurston norm

Abstract Let $L$ be an $n$-component link ($n>1$) with pairwise nonzero linking numbers in a rational homology $3$-sphere $Y$. Assume the complement $X:=Y\setminus \nu (L)$ has nondegenerate Thurston norm. We study when norm-minimizing surface $S$ properly embedded $X$ remains after Dehn filling all boundary components of according to $\partial S$ and capping off by disks. In particular, for $n=2$ capped-off is $[S]$ lies outside finite set rays $H_2(X,\partial X;{\mathbb {R}})$, answering conjecture Gabai. When $Y$ integer sphere this gives upper bound on number surgeries which may yield $S^1\times S^2$. The main techniques come from Gabai’s proof Property R related work.