A compactification of outer space which is an absolute retract

2015/12/09 by Bestvina, Mladen, Horbez, Camille · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1512.02893

Abstract

We define a new compactification of outer space CV_N (the Pacman compactification) which is an absolute retract, for which the boundary is a Z-set. The classical compactification CV_N made of very small F_N-actions on ℝ-trees, however, fails to be locally 4-connected as soon as N≥ 4. The Pacman compactification is a blow-up of CV_N, obtained by assigning an orientation to every arc with nontrivial stabilizer in the trees.

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