Crowell's state space is connected
Daniel Selahi Durusoy

TL;DR
This paper proves that the set of Crowell states for prime alternating knots is connected, providing new insights into knot state spaces and offering a novel proof of a classification result for certain torus knots.
Contribution
It establishes the connectedness of Crowell's state space for prime alternating knots and offers a new proof of a classification theorem for (2,2n+1) torus knots.
Findings
Crowell's state space for prime alternating knots is connected.
Connectedness similar to Kauffman states.
New proof of Ozsvath and Szabo's classification of (2,2n+1) torus knots.
Abstract
We study the set of Crowell states for alternating knot projections and show that for prime alternating knots the space of states for a reduced projection is connected, a result similar to that for Kauffman states. As an application we give a new proof of a result of Ozsvath and Szabo characterizing (2,2n+1) torus knots among alternating knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Computability, Logic, AI Algorithms
