Spheres and projections for Out(Fn)
Spheres and projections for Out(Fn)
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DOI：
10.1112/jtopol/jtu015
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发表时间：
2011-09
影响因子：
1.1
通讯作者：
U. Hamenstädt;S. Hensel
中科院分区：
文献类型：
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作者：
U. Hamenstädt;S. Hensel
2g生成元上自由群的外自同构群Out(F2g)自然包含穿孔亏格g曲面Sg，1的映射类群作为子群.我们定义了S_1×S_2的n个副本的连通和的球面复形到S_g，1的弧形复形中的‘次表面投影’。利用这一点，我们证明了映射(Sg，1)是OUT(F2g)的Lipschitz收缩。我们用另一种“亚表面投影”给出了Handel和Mosher[‘Lipschitz Retrision and Desition for Subgroup of Out(Fn)’，Geom]的一个结果的一个简单证明。白杨。17(2013)1535-1580]指出自由分裂的共轭类稳定剂和自由群FN中的软木1自由因子是自由群FN的Lipschitz收缩(FN)。
The outer automorphism group Out(F2g) of a free group on 2g generators naturally contains the mapping class group of a punctured genus g surface Sg,1 as a subgroup. We define a ‘subsurface projection’ of the sphere complex of the connected sum of n copies of S1×S2 into the arc complex of Sg,1 . Using this, we show that Map(Sg,1) is a Lipschitz retract of Out(F2g) . We use another ‘subsurface projection’ to give a simple proof of a result of Handel and Mosher [‘Lipschitz retraction and distortion for subgroups of Out(Fn) ’, Geom. Topol. 17 (2013) 1535–1580] stating that stabilizers of conjugacy classes of free splittings and corank 1 free factors in a free group Fn are Lipschitz retracts of Out(Fn) .