ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57, 51, 20 Estévez, José-Luis, Universidad Nacional de Educación a Distancia, Spain A Presentation for the Mapping Class Group of a non-orientable surface from Hatcher and Thurston’s Let M be the connected sum of a sphere with k projective planes (k ≥ 3). We consider a normal form for M. A maximal collection of embedded circles in M, say ⟨C_{1}, .., C_{g}⟩, we shall call a +cut − system, so M − {C_{1}, .., C_{g}} is a Klein bottle or a projective plane with 2g holes. We study the graph of Hatcher and Thurston in the non-orientable case, say Z_{g}, and we prove that Z_{g} is connected and simply connected. From this fact and the study of π_{0}Diff(M − {C_{1}, .., C_{g}}), we get, as in the Hatcher-Thurston’s paper, a presentation for the Mapping Class Group of M. References: A Hatcher, and W. Thurston, A presentation for the Mapping Class Group of a closed orientable surface, Topology. 19(1980), 221-237