All exceptional surgeries on alternating knots are integral surgeries

TL;DR

This paper proves that for hyperbolic alternating knots in the 3-sphere, all exceptional surgeries are necessarily integral, providing a complete classification of such surgeries.

Contribution

It establishes that every exceptional surgery on hyperbolic alternating knots must be an integral surgery, resolving a significant question in knot theory.

Findings

All exceptional surgeries on hyperbolic alternating knots are integral.

The result narrows down the possibilities for exceptional surgeries on these knots.

Provides a classification that aids in understanding the structure of hyperbolic alternating knots.

Abstract

We show that all exceptional surgeries on hyperbolic alternating knots in the 3-sphere are integral surgeries.