A four-term exact sequence of fundamental groups of orbit configuration spaces

S. K. Roushon

doi:10.1007/s40879-026-00912-6

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arXiv · 2502.19853

A four-term exact sequence of fundamental groups of orbit configuration spaces

S. K. Roushon

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Abstract

We deduce that the fundamental groups of the orbit configuration spaces of an effective and properly discontinuous action of a discrete group on a connected aspherical 2-manifold, with isolated fixed points, fit into a four-term exact sequence. This comes as a consequence of the four-term exact sequence of orbifold pure braid groups ([18], [11] and [19]). The proof relates these two exact sequences and also draws a new consequence (Corollary 2.3) on the later one.

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S. K. Roushon. 2025-02-27. A four-term exact sequence of fundamental groups of orbit configuration spaces. https://doi.org/10.1007/s40879-026-00912-6

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