$\mathrm{Out}(F_n)$的球面和投影
Spheres and Projections for $\mathrm{Out}(F_n)$
摘要：
2g生成元上的自由群的外自同构群Out（F_2g）自然包含作为子群的穿孔曲面的映射类群。我们定义了一个球面复形的次表面投影到曲面的弧复形中，并使用它来证明这个子群是Out（F_2g）的Lipschitz收缩。我们还使用地下投影给出了一个简单的证明结果Handel和Mosher [HM 10]指出，稳定的共轭类的自由分裂和corank 1自由因子在一个自由群Fn是Lipschitz收缩出（F_n）。
英文摘要：
The outer automorphism group Out(F_2g) of a free group on 2g generators naturally contains the mapping class group of a punctured surface as a subgroup. We define a subsurface projection of the sphere complex of the connected sum of n copies of S^1 x S^2 into the arc complex of the surface and use this to show that this subgroup is a Lipschitz retract of Out(F_2g). We also use subsurface projections to give a simple proof of a result of Handel and Mosher [HM10] stating that stabilizers of conjugacy classes of free splittings and corank 1 free factors in a free group Fn are Lipschitz retracts of Out(F_n).
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