Almost-quasifibrations and fundamental groups of orbit configuration spaces

2021/11/11 by S K Roushon, Roushon, S K
Mathematics · #14F35 #57R18 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Primary: 55R80 #Secondary: 20F99

paper · pdf · doi:10.48550/arxiv.2111.06159

openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we introduce the notion of a k-almost-quasifibration and give many examples. We also show that a large class of these examples are not quasifibrations. As a consequence, supporting the Asphericity conjecture of [19], we deduce that the fundamental group of the orbit configuration space of an effective and properly discontinuous action of a discrete group, on an aspherical 2-manifold with isolated fixed points is torsion free. Furthermore, if the 2-manifold has at least one puncture then it is poly-free, and hence has an iterated semi-direct product of free groups structure, which generalizes a result of Xicotencatl ([27], Theorem 6.3).

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