Dehn surgeries and rational homology balls

TL;DR

This paper investigates which Dehn surgeries on knots, especially torus knots, can bound rational homology balls, using Heegaard Floer correction terms and lattice-theoretic obstructions to classify such surgeries.

Contribution

It introduces new constraints on Dehn surgeries bounding rational homology balls and classifies specific surgeries on certain torus knots using combined Floer homology and lattice theory.

Findings

Identifies constraints on surgery coefficients for rational homology ball bounds.

Classifies integral surgeries on specific torus knots that bound rational homology balls.

Abstract

We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsv\'ath and Szab\'o's correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then turn our attention to the case of integral surgeries, with particular emphasis on positive torus knots. Finally, combining these results with a lattice-theoretic obstruction based on Donaldon's theorem, we classify which integral surgeries along torus knots of the form $T_{kq\pm 1,q}$ bound rational homology balls.