Whitehead moves for G-trees

Details Whitehead moves for G-trees Whitehead moves for G-trees

2007-10-10

arxiv.org/abs/0710.2107v2

Mathematics

Group Theory

v1: 9 pages; v2: 10 pages, minor revisions and one added reference

Scientific paper

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.

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