Fiber surfaces from alternating states

TL;DR

This paper introduces alternating Kauffman states for links, characterizes when their associated surfaces are fibers, and provides a new proof for a related theorem on homogeneous states, advancing understanding of link fiber surfaces.

Contribution

It defines alternating states for links, characterizes fiber surfaces from these states, and offers a novel proof for a theorem on homogeneous states, enhancing theoretical understanding.

Findings

Characterization of fiber surfaces from alternating states

New proof of a theorem on homogeneous states

Conditions under which state surfaces are fibers

Abstract

In this paper we define alternating Kauffman states of links and we characterize when the induced state surface is a fiber. In addition, we give a different proof of a similar theorem of Futer, Kalfagianni and Purcell on homogeneous states.