Title: Almost-quasifibrations and fundamental groups of orbit configuration spaces
Abstract: 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
[11],
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 ([[16], Theorem 6.3]).
Click arXiv:2111.06159 for the full article.