Geodesic
On diffeomorphisms over nonorientable surfaces standardly embedded in the 4–sphere
Hirose, Susumu1
1Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 109-130
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

For a nonorientable closed surface standardly embedded in the 4–sphere, a diffeomorphism over this surface is extendable if and only if this diffeomorphism preserves the Guillou–Marin quadratic form of this embedded surface.

DOI : 10.2140/agt.2012.12.109
Classification : 57Q45, 20F38, 57N05
Keywords: mapping class group, nonorientable surface, knotted surface, Guillou–Marin quadratic form

Hirose, Susumu  1

1 Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan 
@article{10_2140_agt_2012_12_109,
     author = {Hirose, Susumu},
     title = {On diffeomorphisms over nonorientable surfaces standardly embedded in the 4{\textendash}sphere},
     journal = {Algebraic and Geometric Topology},
     pages = {109--130},
     year = {2012},
     volume = {12},
     number = {1},
     doi = {10.2140/agt.2012.12.109},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.109/}
}
TY  - JOUR
AU  - Hirose, Susumu
TI  - On diffeomorphisms over nonorientable surfaces standardly embedded in the 4–sphere
JO  - Algebraic and Geometric Topology
PY  - 2012
SP  - 109
EP  - 130
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.109/
DO  - 10.2140/agt.2012.12.109
ID  - 10_2140_agt_2012_12_109
ER  - 
%0 Journal Article
%A Hirose, Susumu
%T On diffeomorphisms over nonorientable surfaces standardly embedded in the 4–sphere
%J Algebraic and Geometric Topology
%D 2012
%P 109-130
%V 12
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.109/
%R 10.2140/agt.2012.12.109
%F 10_2140_agt_2012_12_109
Hirose, Susumu. On diffeomorphisms over nonorientable surfaces standardly embedded in the 4–sphere. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 109-130. doi: 10.2140/agt.2012.12.109

[1] J S Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math. 22 (1969) 213

[2] D R J Chillingworth, A finite set of generators for the homeotopy group of a non-orientable surface, Proc. Cambridge Philos. Soc. 65 (1969) 409

[3] L Guillou, A Marin, Une extension d’un théorème de Rohlin sur la signature, C. R. Acad. Sci. Paris Sér. A 285 (1977)

[4] S Hirose, On diffeomorphisms over surfaces trivially embedded in the 4–sphere, Algebr. Geom. Topol. 2 (2002) 791

[5] S Hirose, Surfaces in the complex projective plane and their mapping class groups, Algebr. Geom. Topol. 5 (2005) 577

[6] S Hirose, A Yasuhara, Surfaces in 4–manifolds and their mapping class groups, Topology 47 (2008) 41

[7] D Johnson, The structure of the Torelli group I : A finite set of generators for I, Ann. of Math. 118 (1983) 423

[8] W B R Lickorish, Homeomorphisms of non-orientable two-manifolds, Proc. Cambridge Philos. Soc. 59 (1963) 307

[9] W B R Lickorish, On the homeomorphisms of a non-orientable surface, Proc. Cambridge Philos. Soc. 61 (1965) 61

[10] Y Matsumoto, An elementary proof of Rochlin’s signature theorem and its extension by Guillou and Marin, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 119

[11] J M Montesinos, On twins in the four-sphere I, Quart. J. Math. Oxford Ser. 34 (1983) 171

[12] T Nowik, Immersions of non-orientable surfaces, Topology Appl. 154 (2007) 1881

[13] B Szepietowski, Crosscap slides and the level 2 mapping class group of a nonorientable surface

[14] B Szepietowski, A finite generating set for the level 2 mapping class group of a nonorientable surface

Cité par Sources :