A note on lens space surgeries: orders of fundamental groups versus Seifert genera

TL;DR

This paper investigates the relationship between the order of the fundamental group of lens spaces obtained via surgery on knots and the Seifert genus of those knots, providing insights into lens space surgeries.

Contribution

It establishes a connection between the fundamental group order of lens spaces and the Seifert genus of knots with lens space surgeries, offering new constraints and understanding.

Findings

Identifies bounds relating fundamental group order and Seifert genus.

Provides conditions under which lens space surgeries occur.

Enhances understanding of knot and 3-manifold relationships.

Abstract

Let K be a non-trivial knot in the 3-sphere with a lens space surgery and L(p,q) a lens space obtained by a Dehn surgery on K. We study a relationship between the order of the fundamental group of L(p,q) and the Seifert genus of K.