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

2025/02/27 by S. K. Roushon, Roushon, S. K.
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research

paper · pdf · doi:10.1007/s40879-026-00912-6

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.

Citations

• On configuration spaces, their homology, and Lie algebras
• The Geometries of 3-Manifolds

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