Nous définissons une nouvelle compactification de l’outre espace (la compactification de Pacman) qui est un rétract absolu et dont le bord est un -ensemble. À l’inverse, pour tout , la compactification classique , qui consiste en les actions très petites de sur des arbres réels, n’est pas localement -connexe. La compactification de Pacman est un éclatement de , obtenu en attribuant une orientation à tout arc à stabilisateur non trivial dans ces arbres réels.
We define a new compactification of outer space (the Pacman compactification) which is an absolute retract, for which the boundary is a -set. The classical compactification made of very small -actions on -trees, however, fails to be locally -connected as soon as . The Pacman compactification is a blow-up of , obtained by assigning an orientation to every arc with nontrivial stabilizer in the trees.
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Keywords: Outer space, compactification, absolute retract, $Z$-set, $\protect \text{Out}(F_N)$
Mot clés : Outre espace, compactification, rétract absolu, $Z$-ensemble, $\protect \text{Out}(F_N)$
Bestvina, Mladen 1 ; Horbez, Camille 2
@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}, pages = {2395--2437}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {69}, number = {6}, year = {2019}, doi = {10.5802/aif.3298}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3298/} }
TY - JOUR AU - Bestvina, Mladen AU - Horbez, Camille TI - A compactification of outer space which is an absolute retract JO - Annales de l'Institut Fourier PY - 2019 SP - 2395 EP - 2437 VL - 69 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3298/ DO - 10.5802/aif.3298 LA - en ID - AIF_2019__69_6_2395_0 ER -
%0 Journal Article %A Bestvina, Mladen %A Horbez, Camille %T A compactification of outer space which is an absolute retract %J Annales de l'Institut Fourier %D 2019 %P 2395-2437 %V 69 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3298/ %R 10.5802/aif.3298 %G en %F 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, Tome 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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