On aspherical configuration Lie groupoids

Abstract

The complement of the hyperplanes $\{x_i=x_j\}$, for all $i\ne j$ 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.

14p. arXiv admin note: substantial text overlap with arXiv:2106.08110

References in corpus (1)

• A four-term exact sequence of surface orbifold pure braid groups