A note on genera of band-connected sums that are fibered

TL;DR

This paper proves that when a fibered knot is expressed as a band-connected sum, each component is fibered and the genus inequality holds, extending understanding of fibered knots and their decompositions.

Contribution

It establishes that all summands in a band-connected sum of a fibered knot are themselves fibered, and relates the genus of the sum to its components.

Findings

Each component knot in the sum is fibered.

The genus of the sum is at least the sum of the genera of the components.

Provides a genus inequality for band-connected sums of fibered knots.

Abstract

We show that if a fibered knot $K$ is expressed as a band--connected sum of $K_1, \ldots, K_n$, then each $K_i$ is fibered, and the genus of $K$ is greater than or equal to that of the connected sum of $K_1,\ldots,K_n$.