Classification of Lattices Bounded by Large Surgeries of Knots

Ali Naseri Sadr

Classification of Lattices Bounded by Large Surgeries of Knots

Geometric Topology 2024-04-24 v1

Authors: Ali Naseri Sadr

Abstract

We classify all the lattices realized as the intersection form of a positive definite four manifold with boundary $S_n^3(K)$ for a knot $K$ in the three sphere and a positive integer $n$ greater than $4g_4(K)+3$ . We then use this result to define a concordance invariant and generalize a theorem of Rasmussen on lens space surgeries.

Keywords

lattice classification intersection form positive definite four manifold knot surgery concordance invariant lens space surgery

Cite

@article{arxiv.2404.14633,
  title  = {Classification of Lattices Bounded by Large Surgeries of Knots},
  author = {Ali Naseri Sadr},
  journal= {arXiv preprint arXiv:2404.14633},
  year   = {2024}
}

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