An algorithm for computing the $Υ$-invariant and the $d$-invariants of Dehn surgeries

Taketo Sano, Kouki Sato

Published 2020-02-21Version 1

By using grid homology theory, we give an explicit algorithm for computing Ozsv\'ath-Stipsicz-Szab\'o's $\Upsilon$-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.