Whitehead moves for G‐trees

We generalize the familiar notion of a Whitehead move from Culler and Vogtmann's Outer space to the setting of deformation spaces of G‐trees. Specifically, we show that there are two moves, each of which transforms a reduced G‐tree into another reduced G‐tree, that suffice to relate any two reduced trees in the same deformation space. These two moves further factor into three moves between reduced trees that have simple descriptions in terms of graphs of groups. This result has several applications.

我们将库勒（Culler）和沃格特曼（Vogtmann）的外空间中熟悉的怀特黑德（Whitehead）移动概念推广到G - 树的形变空间的情形。具体而言，我们表明存在两种移动，每种移动都能将一棵简约的G - 树变换为另一棵简约的G - 树，这两种移动足以将同一形变空间中的任意两棵简约树联系起来。这两种移动进一步分解为简约树之间的三种移动，这些移动在群图方面有简单的描述。这个结果有若干应用。