On homotopy braids
V. G. Bardakov, V.V.Vershinin, Jie Wu
TL;DR
This paper investigates the properties of the homotopy braid group, proving its linearity over integers and torsion-freeness for three strands, advancing understanding of its algebraic structure.
Contribution
It establishes the linearity of the homotopy braid group over integers and proves torsion-freeness for the three-strand case, providing new insights into its algebraic properties.
Findings
Homotopy braid group is linear over the integers.
Homotopy braid group on three strands is torsion free.
Advances understanding of algebraic structure of homotopy braid groups.
Abstract
Homotopy braid group is the subject of the paper. First, linearity of homotopy braid group over the integers is proved. Then we prove that the group homotopy braid group on three strands is torsion free.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications