风车和极端2-细胞
Windmills and extreme 2-cells
摘要：
在这篇文章中，我们证明了新的结果存在的2-细胞在圆盘图是极端的意义上，他们被附加到其余的图沿一个小的连接部分的边界循环。特别是，我们建立的条件，2复杂的X，这意味着所有的最小面积圆盘图在X减少边界圈有极端的2细胞在这个意义上。极端2细胞在这些复杂的圆盘图中的存在导致新的结果的一致性使用周长减少技术，我们在以前的文章中开发。回想一下，一个群被称为凝聚的，如果它的所有生成的子群都是连续的。我们说明了这种方法表明，几个类的一个relator组，小取消组和交错介绍组的集合连贯的群体。
英文摘要：
In this article we prove new results about the existence of 2-cells in disc diagrams which are extreme in the sense that they are attached to the rest of the diagram along a small connected portion of their boundary cycle. In particular, we establish conditions on a 2-complex X which imply that all minimal area disc diagrams over X with reduced boundary cycles have extreme 2-cells in this sense. The existence of extreme 2-cells in disc diagrams over these complexes leads to new results on coherence using the perimeter-reduction techniques we developed in an earlier article. Recall that a group is called coherent if all of its finitely generated subgroups are finitely presented. We illustrate this approach by showing that several classes of one-relator groups, small cancellation groups and groups with staggered presentations are collections of coherent groups.
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