Geodesic
Abelian subgroups generated by Dehn twists in homeomorphism group
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2013), pp. 26-32
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The subgroup of mapping class group generated by Dehn twists along the set of simple closed pairwise nonhomotopic curves with some conditions is studied. It is proved that this group is isomorphic to a free Abelian group of rank $k$, where $k$ is the number of curves in the set. In the case of an oriented surface, this result is classic. 
@article{VMUMM_2013_1_a4,
     author = {D. A. Permyakov},
     title = {Abelian subgroups generated by {Dehn} twists in homeomorphism group},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {26--32},
     year = {2013},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_1_a4/}
}
TY  - JOUR
AU  - D. A. Permyakov
TI  - Abelian subgroups generated by Dehn twists in homeomorphism group
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2013
SP  - 26
EP  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2013_1_a4/
LA  - ru
ID  - VMUMM_2013_1_a4
ER  - 
%0 Journal Article
%A D. A. Permyakov
%T Abelian subgroups generated by Dehn twists in homeomorphism group
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2013
%P 26-32
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2013_1_a4/
%G ru
%F VMUMM_2013_1_a4
D. A. Permyakov. Abelian subgroups generated by Dehn twists in homeomorphism group. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2013), pp. 26-32. http://geodesic.mathdoc.fr/item/VMUMM_2013_1_a4/

[1] Dehn M., “Die Gruppe der Abbildungsklassen”, Acta Math., 69:1 (1938), 135–206 | DOI | MR

[2] Farb B., Margalit D., A primer on mapping class groups, http://www.math.utah.edu/m̃argalit/primer | MR

[3] Birman J.S., Lubotzky A., McCarthy J., “Abelian and solvable subgroups of the mapping class group”, Duke Math. J., 50 (1983), 1107–1120 | DOI | MR

[4] Kudryavtseva E.A., Permyakov D.A., “Osnaschennye funktsii Morsa na poverkhnostyakh”, Matem. sb., 201:4 (2010), 33–98 | DOI

[5] Kudryavtseva E.A., O gomotopicheskom tipe prostranstv funktsii Morsa na poverkhnostyakh, arXiv: 1104.4796

[6] Kudryavtseva E.A., Topologiya prostranstv funktsii Morsa na poverkhnostyakh, arXiv: 1104.4792

[7] Kudryavtseva E.A., Spetsialnye osnaschennye funktsii Morsa na poverkhnostyakh, arXiv: 1106.3116

[8] Duchin M., Rafi K., “Divergence of Geodesics in Teichmüller space and the Mapping Class Group”, Geometric and Funct. Anal., 19:3 (2009), 722–742 | DOI | MR

[9] Lyndon R., Schupp P.E., Combinatorial group theory, Springer-Verlag, Berlin, 1977 | MR