论文标题
尼尔森（Nielsen）实现了3个manifolds的球体
Nielsen Realization for sphere twists on 3-manifolds
论文作者
论文摘要
对于3个manifold M，扭曲组扭曲（M）是twist围绕嵌入式2个spheres生成的映射类组MOD（M）的子组。我们研究了扭曲亚组（M）的尼尔森实现问题。我们证明，当且仅当G是循环并且M是透镜空间的连接之和时，我们证明非平凡的亚组G <twist（M）是通过差异性实现的。我们还将我们的方法应用于3个manifolds的Burnside问题，并表明当M可还原时，DIFF（M）不包含无限的扭转组，而不是连接的镜头空间之和。
For a 3-manifold M, the twist group Twist(M) is the subgroup of the mapping class group Mod(M) generated by twists about embedded 2-spheres. We study the Nielsen realization problem for subgroups of Twist(M). We prove that a nontrivial subgroup G<Twist(M) is realized by diffeomorphisms if and only if G is cyclic and M is a connected sum of lens spaces. We also apply our methods to the Burnside problem for 3-manifolds and show that Diff(M) does not contain an infinite torsion group when M is reducible and not a connected sum of lens spaces.
