Dehn surgeries that yield fibred $3$--manifolds

TL;DR

This paper investigates specific Dehn surgeries on null-homotopic knots that produce fibred 3-manifolds under certain homological conditions, using sutured manifold theory, and explores surgeries affecting the Thurston norm.

Contribution

It provides new insights into which Dehn surgeries yield fibred 3-manifolds and how surgeries can alter the Thurston norm of fibred manifolds, addressing questions in 3-manifold topology.

Findings

Identifies conditions under which Dehn surgeries produce fibred 3-manifolds.

Shows surgeries that reduce the Thurston norm of fibred manifolds.

Provides negative examples to a question of Michel Boileau.

Abstract

We study Dehn surgeries on null-homotopic knots that yield fibred $3$--manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai's theory of sutured manifold decomposition. Such surgeries are negative examples to a question of Michel Boileau. Another result we will prove is about surgeries which reduce the Thurston norm of a fibred manifold.