Homotopy invariants of Gauss phrases
Andrew Gibson
TL;DR
This paper introduces new invariants for Gauss phrases under homotopy and open homotopy equivalence relations, expanding the understanding of their combinatorial properties.
Contribution
It defines novel invariants for Gauss phrases and characterizes their possible values under two related equivalence relations.
Findings
New invariants for Gauss phrases are established.
The possible values of these invariants are fully characterized.
The work deepens the understanding of Gauss phrase equivalence classes.
Abstract
Equivalence relations can be defined on Gauss phrases using combinatorial moves. In this paper we consider two closely related equivalence relations on Gauss phrases, homotopy and open homotopy. In particular, in each case, we define a new invariant and determine the values that it can attain.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics