Obstructing finite surgery

TL;DR

This paper proves that for a fixed surgery parameter p, only finitely many elliptic 3-manifolds can be obtained from p/q-surgery on knots in S^3, using Heegaard Floer invariants to obstruct certain manifolds.

Contribution

It establishes a finiteness result for elliptic 3-manifolds obtained via knot surgery, employing Heegaard Floer correction terms as obstructions.

Findings

Finiteness of elliptic manifolds from fixed p/q-surgery

Use of Heegaard Floer d-invariants as obstructions

New constraints on knot surgeries producing elliptic manifolds

Abstract

For a fixed p, there are only finitely many elliptic 3-manifolds given by p/q-surgery on a knot in S^3. We prove this result by using the Heegaard Floer correction terms (d-invariants) to obstruct elliptic manifolds from arising as knot surgery.