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

Taketo Sano; Kouki Sato

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

Geometric Topology 2020-02-24 v1

Authors: Taketo Sano , Kouki Sato

Abstract

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.

Keywords

dehn surgery

Cite

@article{arxiv.2002.09210,
  title  = {An algorithm for computing the $\Upsilon$-invariant and the $d$-invariants of Dehn surgeries},
  author = {Taketo Sano and Kouki Sato},
  journal= {arXiv preprint arXiv:2002.09210},
  year   = {2020}
}

Comments

38 pages, 5 figures

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