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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.40 no.2 Bogotá July./Dec. 2006

 

ON THE HOMEOTOPY GROUP OF THE NON ORIENTABLE SURFACE OF GENUS THREE

 

Francisco Javier González-Acuña*, Juan Manuel Márquez-Bobadilla**

* Universidad Nacional Autónoma de Mexico, México

Instituto de Matemáticas UNAM and CIMAT Circuito Interior S/N, Ciudad Universitaria, 04510 C.P. 3600 México D.F., México

e-mail: ficomx@yahoo.com.mx

** Universidad de Guadalajara, México

Departamento de Matemáticas CUCEI-Universidad de Guadalajara and CIMAT A.C. Callejón Jalisco S/N Valenciana, 36240 A.P. 402 Guanajuanto, México

e-mail: juanm@cimat.mx


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).

Keywords and phrases. Homeotopy group, non-orientable surface.

2000 Mathematics Subject Classification. Primary: 57M60. Secondary: 20F38.


Resumen. 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).


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(Recibido en mayo de 2006. Aceptado en julio de 2006)

 

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