English

On definite lattices bounded by integer surgeries along knots with slice genus at most 2

Geometric Topology 2024-09-09 v2

Abstract

We classify the positive definite intersection forms that arise from smooth 4-manifolds with torsion-free homology bounded by positive integer surgeries on the right-handed trefoil. A similar, slightly less complete classification is given for the (2,5)-torus knot, and analogous results are obtained for integer surgeries on knots of slice genus at most two. The proofs use input from Yang--Mills instanton gauge theory and Heegaard Floer correction terms.

Keywords

Cite

@article{arxiv.1807.11931,
  title  = {On definite lattices bounded by integer surgeries along knots with slice genus at most 2},
  author = {Marco Golla and Christopher Scaduto},
  journal= {arXiv preprint arXiv:1807.11931},
  year   = {2024}
}

Comments

20 pages, 6 figures; final version, to appear in the Transactions of the AMS