Geodesic
On the dimension of the mapping class groups of a non-orientable surface
Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 347-372.

Voir la notice de l'article provenant de la source International Press of Boston

Let $\mathcal{N}_g$ be the mapping class group of a non-orientable closed surface. We prove that the proper cohomological dimension, the proper geometric dimension, and the virtual cohomological dimension of $\mathcal{N}_g$ are equal whenever $g \neq 4,5$. In particular, there exists a model for the classifying space of $\mathcal{N}_g$ for proper actions of dimension $\operatorname{vcd}(\mathcal{N}_g)=2g-5$. Similar results are obtained for the mapping class group of a non-orientable surface with boundaries and possibly punctures, and for the pure mapping class group of a non-orientable surface with punctures and without boundaries.
DOI : 10.4310/HHA.2022.v24.n1.a17
Classification : 20F34, 20F65, 20J05
Keywords: mapping class group, non-orientable surface, virtual cohomological dimension, proper cohomological dimension, proper geometric dimension 
@article{HHA_2022_24_1_a16,
     author = {Cristhian E. Hidber and Luis Jorge S\'anchez Salda\~na and Alejandra Trujillo-Negrete},
     title = {On the dimension of the mapping class groups of a non-orientable surface},
     journal = {Homology, homotopy, and applications},
     pages = {347--372},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2022},
     doi = {10.4310/HHA.2022.v24.n1.a17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a17/}
}
TY  - JOUR
AU  - Cristhian E. Hidber
AU  - Luis Jorge Sánchez Saldaña
AU  - Alejandra Trujillo-Negrete
TI  - On the dimension of the mapping class groups of a non-orientable surface
JO  - Homology, homotopy, and applications
PY  - 2022
SP  - 347
EP  - 372
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a17/
DO  - 10.4310/HHA.2022.v24.n1.a17
LA  - en
ID  - HHA_2022_24_1_a16
ER  - 
%0 Journal Article
%A Cristhian E. Hidber
%A Luis Jorge Sánchez Saldaña
%A Alejandra Trujillo-Negrete
%T On the dimension of the mapping class groups of a non-orientable surface
%J Homology, homotopy, and applications
%D 2022
%P 347-372
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a17/
%R 10.4310/HHA.2022.v24.n1.a17
%G en
%F HHA_2022_24_1_a16
Cristhian E. Hidber; Luis Jorge Sánchez Saldaña; Alejandra Trujillo-Negrete. On the dimension of the mapping class groups of a non-orientable surface. Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 347-372. doi : 10.4310/HHA.2022.v24.n1.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a17/

Cité par Sources :