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<p>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 established by Flechsig and Roushon. The proof relates these two exact sequences and also draws a new consequence (Corollary 2.3) on the later one.</p>

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

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • S. K. Roushon

摘要

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 established by Flechsig and Roushon. The proof relates these two exact sequences and also draws a new consequence (Corollary 2.3) on the later one.