no. 6
A compactification of outer space which is an absolute retract
Bestvina, Mladen1; Horbez, Camille2
1 Department of Mathematics, University of Utah 155 South 1400 East, JWB 233 Salt Lake City, Utah 84112-0090 (USA)
2 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS, Université Paris-Saclay 91405 Orsay (France)
Annales de l'Institut Fourier, Volume 69 (2019) no. 6, pp. 2395-2437.

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.

Nous définissons une nouvelle compactification de l’outre espace CV N (la compactification de Pacman) qui est un rétract absolu et dont le bord est un Z-ensemble. À l’inverse, pour tout N≥4, la compactification classique CV N ¯, qui consiste en les actions très petites de F N sur des arbres réels, n’est pas localement 4-connexe. La compactification de Pacman est un éclatement de CV N ¯, obtenu en attribuant une orientation à tout arc à stabilisateur non trivial dans ces arbres réels.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3298
Classification: 20E36
Keywords: Outer space, compactification, absolute retract, $Z$-set, $\protect \text{Out}(F_N)$
Bestvina, Mladen 1; Horbez, Camille 2

1 Department of Mathematics, University of Utah 155 South 1400 East, JWB 233 Salt Lake City, Utah 84112-0090 (USA)
2 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS, Université Paris-Saclay 91405 Orsay (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Bestvina, Mladen; Horbez, Camille. A compactification of outer space which is an absolute retract. Annales de l'Institut Fourier, Volume 69 (2019) no. 6, pp. 2395-2437. doi : 10.5802/aif.3298. https://aif.centre-mersenne.org/articles/10.5802/aif.3298/

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