Almost-quasifibrations and fundamental groups of orbit configuration spaces
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).
Keywords
Cite
@article{arxiv.2111.06159,
title = {Almost-quasifibrations and fundamental groups of orbit configuration spaces},
author = {S K Roushon},
journal= {arXiv preprint arXiv:2111.06159},
year = {2025}
}
Comments
The paper is withdrawn. Due to corrections in arXiv:2006.07106 and in arXiv:2106.08110, the main result Theorem 1.3 is not valid