An algorithm for computing the ${\rm Y}$-invariant and the $d$-invariants of Dehn surgeries

Abstract

By using grid homology theory, we give an explicit algorithm for computing Ozsváth-Stipsicz-Szabó's ${\rm Y}$-invariant and the $d$-invariant of Dehn surgeries along knots in $S^3$. As its application, we compute the two invariants for all prime knots with up to 11 crossings.

38 pages, 5 figures