论文标题
配置lie lie groupoids和orbifold辫子组
Configuration Lie groupoids and orbifold braid groups
论文作者
论文摘要
我们提出了两个构型lie groupoids的定义，在这两种情况下，我们都证明了一类lie groupoids的Fadell-Neuwirth型纤维定理。我们表明，这是最好的扩展，从某种意义上说，对于与具有非空的单数集合的全球符号相对应的lie groupoids，振动定理不存在。其次，我们证明了基本组（称为{\ it pure Orbifold辫子组}}的简短精确序列，属于lie groupoid的一个配置lie lie lie lie lie lie lie clopoids，与带锥体点的刺穿的复杂平面相对应。这显示了对lie群体类型的列型型fadell-neuwirth定理的可能性。结果，首先，我们看到纯的Orbifold辫子组具有多重自由结构，这概括了经典的编织组案例。我们还提供了纯Orbifold编织组的一组明确的发电机。其次，我们证明了一类仿射和有限的复杂的artin组几乎不含多个元素，这部分回答了所有Artin组是否实际上不含多重的问题（[[4]，问题2]）。最后，结合了这种多重自由结构和最近的结果（[5]），我们推断了上述Orbifold辫子组的Farrell-Jones同构猜想。这也意味着对$ \ tilde d_n $类型的Artin Artin组的猜想，该组在[[24]，问题]中被打开。
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].
