椭圆图中的距离
Distance in the Ellipticity Graph
摘要：
定义了自由群$F$的椭圆度图. Kapovich和M. Lustig为了研究作用在此图上的$F$的外自同构群而提出了一种新的方法。该图被构造成类似于曲面的曲线复合体。它是一个二部图，其顶点是$F$的非平凡元素的共轭类和形式为$F=A*B$的真自由积分解的等价类。只要共轭类在$A$或$B$中有代表，共轭类就通过边连接到自由积分解$A*B$.本文使用Stallings子群$X$ -有向图和Whitehead自同构构造算法，确定当两个顶点之间的椭圆度图的距离是2，这两种类型的顶点。
英文摘要：
The ellipticity graph of a free group $F$ was defined by I. Kapovich and M. Lustig in order to study the outer automorphism group of $F$, which acts on this graph. The graph was constructed to be analogous to the curve complex of a surface. It is a bipartite graph, whose vertices are conjugacy classes of nontrivial elements of $F$ and equivalence classes of proper free product decompositions of the form $F=A*B$. A conjugacy class is joined by an edge to a free product decomposition $A*B$ whenever the conjugacy class has a representative in either $A$ or $B$. This paper uses Stallings subgroup $X$-digraphs and Whitehead automorphisms to construct algorithms that determine when the distance between two vertices of the ellipticity graph is two, for both types of vertices.
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