Surgeries on Iterated Torus Knots Bounding Rational Homology 4-Balls

TL;DR

This paper classifies certain surgeries on algebraic knots that bound rational homology 4-balls, using explicit plumbing descriptions and Donaldson's Theorem to identify cases with specific knot parameters.

Contribution

It provides an explicit description of 4-manifolds bounding large surgeries on algebraic knots and classifies those that bound rational homology 4-balls using lattice embedding obstructions.

Findings

Large surgeries on algebraic knots bound negative definite plumbings.

Classification of surgeries bounding rational homology 4-balls based on knot parameters.

Application of Donaldson's Theorem to obstruct certain 4-manifold embeddings.

Abstract

We show that all large enough positive integral surgeries on algebraic knots bound a 4-manifold with a negative definite plumbing tree, which we describe explicitly. Then we apply the lattice embedding obstruction coming from Donaldson's Theorem to classify the ones of the form $S^3_n(T(p_1,k_1p_1+1; p_2, k_2p_2\pm 1))$ that also bound rational homology 4-balls.