A Theory of Orbit Braids

Abstract

In this paper, the authors systematically discuss orbit braids in M × I with regards to orbit configuration space F _G(M, n), where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G. These orbit braids form a group, named orbit braid group, which enriches the theory of ordinary braids.

The authors analyze the substantial relations among various braid groups associated to those configuration spaces F _G(M, n), F(M/G, n) and F(M, n). They also consider the presentations of orbit braid groups in terms of orbit braids as generators by choosing M = ℂ with typical actions of ℤ _p and (ℤ₂)².

Keywords

Orbit braid / Orbit configuration space

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