Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
On the homeotopy group of the non orientable surface of genus three
Palabras clave:
Homeotopy group, Non-orientable surface, 2000 Mathematics Subject Classification, Primary: 57M60, Secondary: 20F38 (en)Descargas
Abstract. In this note we prove that, if N3 = P#P#P, where P : = RP2, then the canonical homomorphism from Diff (N3) onto the homeotopy group Mod(N3) has a section. To do this we first prove that Mod(N3 ) = GL(2, Z).
En esta nota probamos que, si N3 = P#P#P, donde P : = RP2, entonces el homomorfismo canónico de Diff (N3) sobre el grupo de homeotopía Mod(N3) tiene una sección. Para hacer esto, primero probamos que Mod(N3) = GL(2, Z).
Referencias
S. Akbulut & H. King, Submanifolds and the homology of non singular algebraic varieties, Amer. J. Math., 107 (1985), 45-83.
J. S. Birman & D. R. J. Chillingworth, On the homeotopy group of a non-orientable surface, Proc. Camb. Phil. Soc., 71 (1972), 437-448.
J. S. Birman & M. H. Hilden, Lifting and projecting homeomorphisms, Arch. Math., 23 (1972), 428-434.
D. B. A. Epstein, Curves on 2 —manifolds and isotopies, Acta Math., 115 (1966), 83-107.
N. V. Ivanov, Mapping Class Groups, Handbook of Geometric Topology, Elsevier Science, N.H. (2002), 523-633.
W. B. R. Lickorish, Homeomorphisms of non-orientable two-manifolds, Math. Proc. Camb. Phil. Soc., 59 (1963), 307-317.
J. M. Márquez, On the trigenus of surface bundles over S^1, Aportaciones Matemáticas, 35 (2005), 201-215.
G. Mikhalkin, Blowup equivalence of smooth closed manifolds, Topology, 36 (1997), 287-299.
Sh. Morita, Characteristic classes of surface bundles, Bull. Amer. Math. Soc., 11 (1984) 2, 386-388.
Sh. Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987) 3, 552-577.
D. Rolfsen, Knots and links, Math. Lectures Series. 7. Berkeley, Ca. Publish Perish, Inc. 1976. [12] H. Torriani, Subgroups of the Klein bottle group and the mapping class group of the Klein Bottle, Rend. Mat. Appl., 7 (1987) 7, 215-222.
