Stability of the homology of the mapping class groups of orientable surfaces
Stability of the homology of the mapping class groups of orientable surfaces
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DOI：
10.2307/1971172
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发表时间：
1985-03
影响因子：
4.9
通讯作者：
J. Harer
中科院分区：
文献类型：
--
作者：
J. Harer
F = Fgsr的映射类群为F = rgs = wo（A），其中A是F的保向同态的拓扑群，它们是dF上的恒等式，固定s-穿孔.当r = 0且2g + s > 3时，F的一个重要特征是它适当地不连续地作用在Teichmiller空间US上;商是模空间。F上的有限面积完全双曲度量的等距类。由于US与欧几里得空间同胚，并且F实际上是无挠的，我们有
The mapping class group of F = Fgs r is F = rgs = wo(A) where A is the topological group of orientation preserving diffeomorphisms of F which are the identity on dF and fix the s punctures. When r = 0 and 2g + s > 3, an important feature of F is that it acts properly discontinuously on the Teichmiller space US; the quotient is the moduli space .#f of isometry classes of complete hyperbolic metrics of finite area on F. Since US is homeomorphic to Euclidean space and F is virtually torsion-free, we have