论文标题
四面体Coxeter组，3个manifolds上的大型集体活动和近似Heegaard分裂
Tetrahedral Coxeter groups, large group-actions on 3-manifolds and equivariant Heegaard splittings
论文作者
论文摘要
我们考虑在封闭的，可定向和不可定向的3个manifolds M上进行有限的群体行为，该m保留了某些G> 1的M的Heegaard分裂的两个手柄（也许可以互换两个手柄）。在g> 1属的手柄上有限的小组成分的最大可能顺序为12（g-1），在定向呈现案例中，通常为24（g-1），并且通常是24（g-1），并且保留了保留heegaard g属Heegaard表面的有限组的最大顺序为48（g-1）。这定义了我们在本文中讨论的3个manifolds的有限群体行为的层次结构；我们以48型（G-1）的作用表示各种歧管，对于G的小值，尤其是独特的双曲线3个manifold，具有最小的可能属G = 6的作用（与3道毛的欧几里得病例相比，具有G = 3的欧几里得病例，具有这种作用）。
We consider finite group-actions on closed, orientable and nonorientable 3-manifolds M which preserve the two handlebodies of a Heegaard splitting of M of some genus g > 1 (maybe interchanging the two handlebodies). The maximal possible order of a finite group-action on a handlebody of genus g>1 is 12(g-1) in the orientation-preserving case and 24(g-1) in general, and the maximal order of a finite group preserving the Heegaard surface of a Heegaard splitting of genus g is 48(g-1). This defines a hierarchy for finite group-actions on 3-manifolds which we discuss in the present paper; we present various manifolds with an action of type 48(g-1) for small values of g, and in particular the unique hyperbolic 3-manifold with such an action of smallest possible genus g = 6 (in strong analogy with the Euclidean case of the 3-torus which has such actions for g = 3).
