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S K Roushon

Publications and source records attributed to S K Roushon.

6 recordsLinked to original sources
arXiv2025

Configuration Lie groupoids and orbifold braid groups

We propose two definitions of configuration Lie groupoids and in both the cases we prove a Fadell-Neuwirth type fibration theorem for a class of Lie groupoids. We show that this is the best possible extension, in the sense that, for the class of Lie groupoids corresponding to global quotient orbifolds with nonempty singular set, the fibration theorems do not hold. Secondly, we prove a short exact sequence of fundamental groups (called {\it pure orbifold braid groups}) of one of the configuration Lie groupoids of the Lie groupoid corresponding to the punctured complex plane with cone points. This shows the possibility of a quasifibration type Fadell-Neuwirth theorem for Lie groupoids. As consequences, first we see that the pure orbifold braid groups have poly-virtually free structure, which generalizes the classical braid group case. We also provide an explicit set of generators of the pure orbifold braid groups. Secondly, we prove that a class of affine and finite complex Artin groups are virtually poly-free, which partially answers the question if all Artin groups are virtually poly-free ([[4], Question 2]). Finally, combining this poly-virtually free structure and a recent result ([5]), we deduce the Farrell-Jones isomorphism conjecture for the above class of orbifold braid groups. This also implies the conjecture for the case of the affine Artin group of type $\tilde D_n$, which was left open in [[24], Problem].

math.GT↗
arXiv2025

Almost-quasifibrations and fundamental groups of orbit configuration spaces

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).

math.GT↗
arXiv2024

On aspherical configuration Lie groupoids

The complement of the hyperplanes $\{x_i=x_j\}$, for all $i\neq j$ in $M^n$, for $M$ an aspherical $2$-manifold, is known to be aspherical. Here we consider the situation, when $M$ is a $2$-dimensional orbifold. We prove this complement to be aspherical for a class of aspherical $2$-dimensional orbifolds, and predict that it should be true in general also. We generalize this question in the category of Lie groupoids, as orbifolds can be identified with a certain kind of Lie groupoids.

math.AT↗
arXiv2020

Some virtually poly-free Artin groups

In this short note we prove that a class of Artin groups of affine and complex types are virtually poly-free, answering partially the question if all Artin groups are virtually poly-free.

math.GR↗