Orbit configuration spaces associated to discrete subgroups of PSL(2,R)
Orbit configuration spaces associated to discrete subgroups of PSL(2,R)
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DOI：
10.1016/j.jpaa.2009.04.003
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发表时间：
2009-12
影响因子：
0.8
通讯作者：
F. R. Cohen;Toshiyuki Kohno;M. Xicoténcatl
中科院分区：
文献类型：
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作者：
F. R. Cohen;Toshiyuki Kohno;M. Xicoténcatl
本文的目的是分析由群G自由作用且在上半平面H2上适当间断地得到的几个与“轨道构形空间”相关的李代数。从相关基本群的降序中心级数得到的李代数被证明是同构的，直到重新分级，所得到的李代数类似于[T.Kohno，辫子群的线性表示和经典的Yang-Baxter方程]中所研究的李代数。数学课。78(1988)339-363；T.Kohno，Vassiliev不变量和De Rham复形在纽结空间上，沉思。数学课。179(1994)123-138；T.Kohno，椭圆KZ系统，环面编织群和Vassiliev不变量，拓扑学及其应用78(1997)79-94；D.C.Cohen，纤维型排列和轨道构形空间的单一性，论坛数学。13(2001)505-530；F.R.Cohen，M.Xicoténcatl，关于与高斯整数有关的轨道配置空间：同调和同伦群，拓扑学应用。118(2002)17-29；E.Fadell和S.Husseini，位形空间上的环空间和Majer-Terracini指数，Topol。方法采用非线性分析方法。J.Julius Schauder Center 11(1998)，249-271；E.Fadell和S.Husseini，几何和拓扑学，in：Springer-Verlag，2001；F.R.Cohen和T.Sato，On Groups of CoAlgebras，(提交出版)]。文中还讨论了一个相关的分次Poisson代数的结构，该分次Poisson代数是由参数化为G的无穷小辫子关系的类比得到的。
The purpose of this article is to analyze several Lie algebras associated to “orbit configuration spaces” obtained from a group G acting freely, and properly discontinuously on the upper half-plane H2. The Lie algebra obtained from the descending central series for the associated fundamental group is shown to be isomorphic, up to a regrading, to The resulting Lie algebras are similar to those studied in [T. Kohno, Linear representations of braid groups and classical Yang-Baxter equations, Contemp. Math. 78 (1988) 339–363; T. Kohno, Vassiliev invariants and de Rham complex on the space of knots, Contemp. Math. 179 (1994) 123–138; T. Kohno, Elliptic KZ system, braid groups of the torus and Vassiliev invariants, Topology and its Applications 78 (1997) 79–94; D.C. Cohen, Monodromy of fiber-type arrangements and orbit configuration spaces, Forum Math. 13 (2001) 505–530; F.R. Cohen, M. Xicoténcatl, On orbit configuration spaces associated to the Gaussian integers: homology and homotopy groups, Topology Appl. 118 (2002) 17–29; E. Fadell and S. Husseini, The space of loops on configuration spaces and the Majer-Terracini index, Topol. Methods Nonlinear Anal. J. Julius Schauder Center 11 (1998), 249–271; E. Fadell and S. Husseini, Geometry and Topology of Configuration Spaces, in: Springer Monographs in Mathematics, Springer-Verlag, 2001; F.R. Cohen and T. Sato, On groups of morphisms of coalgebras, (submitted for publication)]. The structure of a related graded Poisson algebra defined below and obtained from an analogue of the infinitesimal braid relations parametrized by G is also addressed.