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Bulletin of the London Mathematical Society Advance Access originally published online on February 6, 2009
Bulletin of the London Mathematical Society 2009 41(2):205-212; doi:10.1112/blms/bdn118
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© 2009 London Mathematical Society

Whitehead moves for G-trees

Matt Clay and Max Forester

Department of Mathematics
University of Oklahoma
Norman, OK 73019
USA
forester@math.ou.edu

Received 18 September 2007. Revision received 7 October 2008.

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.

2000 Mathematics Subject Classification 20E08 (primary), 20E06, 20F65 (secondary).

The second author is partially supported by NSF grant no. DMS-0605137.


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