A compactification of outer space which is an absolute retract
Annales de l'Institut Fourier, Volume 69 (2019) no. 6, p. 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 : 2016-01-12
Revised : 2017-02-13
Accepted : 2018-11-06
Published online : 2019-10-29
DOI : https://doi.org/10.5802/aif.3298
Classification:  20E36
Keywords: Outer space, compactification, absolute retract, Z-set, Out(F N ) 
@article{AIF_2019__69_6_2395_0,
     author = {Bestvina, Mladen and Horbez, Camille},
     title = {A compactification of outer space which is an absolute retract},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {69},
     number = {6},
     year = {2019},
     pages = {2395-2437},
     doi = {10.5802/aif.3298},
     language = {en},
     url={aif.centre-mersenne.org/item/AIF_2019__69_6_2395_0/}
}

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/item/AIF_2019__69_6_2395_0/

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