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

TL;DR

This paper classifies certain positive definite intersection forms from smooth 4-manifolds bounded by integer surgeries on knots with slice genus at most 2, using gauge theory and Floer homology techniques.

Contribution

It provides a classification of intersection forms for 4-manifolds bounded by surgeries on specific knots with low slice genus, extending previous results.

Findings

Classified intersection forms for surgeries on the right-handed trefoil.

Extended classification to (2,5)-torus knot and knots with slice genus ≤ 2.

Utilized Yang--Mills instanton gauge theory and Heegaard Floer correction terms.

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.