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arXiv · 2106.08110

Quasifibrations in configuration Lie groupoids and orbifold braid groups

S. K. Roushon
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Abstract

In [19] we studied a Fadell-Neuwirth type fibration theorem for orbifolds, and gave a short exact sequence of fundamental groups of configuration Lie groupoids of Lie groupoids corresponding to the genus zero 2-dimensional orbifolds with cone points, and at least one puncture. In this paper we extend this work to all genus $\geq 1$, 2-dimensional orbifolds with cone points. As a consequence, we prove the Farrell-Jones Isomorphism conjecture for the fundamental groups of the associated configuration Lie groupoids. This answers a substantial part of a question we posed in [[18], Problem]. In [19] we also showed that for all global quotient type orbifolds, the fibration theorem does not hold. Here, we give some nontrivial examples of orbifolds where a Fadell-Neuwirth type quasifibration theorem holds. Finally, we state an Asphericity conjecture and a Quasifibration conjecture for orbifolds.

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S. K. Roushon. 2021-06-15. Quasifibrations in configuration Lie groupoids and orbifold braid groups. https://arxiv.org/abs/2106.08110

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