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**Additional info for Algebraic Topology, Aarhus 1978**

**Sample text**

E. the collection of real numbers which occur as lengths of closed geodesies) is discrete. Using this fact, one 30 3. Teichmuller Spaces and Mapping Class Groups can show, without much effort, that the action of the mapping class group T* on the Teichmuller space Tg is properly discontinuous, that is to say, that for every set K C Tg, the collection of $ £ TJ is such that, $ (K) fl K 7^ 0 , is finite. N modulo a finite group. Furthermore, since Msg is rational in /("-theory, we have: H* (M'g;Q) £ H* ( r * ; Q ) .

Teichmiiller Spaces and Mapping Class Groups [5] Benson, D. J. and Cohen, F. : Mapping Class Groups of Low Genus and their Cohomology, Memoirs, American Math. Society Vol 90 Number 443 (1991). : Stability of the Homology of the Mapping Class Group of Orientable Surfaces, Ann. of Math. 121 (1985) 215-249. : Die Gruppe der Abbildungsklasser, Acta Math. 69 (1938) 81-115. : Generators for the Mapping Class Group, in Topology of Low Dimensional Manifolds, Springer-Verlag Lecture Notes in Mathematics Vol.

Di (i > 0) consists of the surfaces with a node at a curve which separates E s into surfaces of genus i and <7 — i. For the genus one case, the Teichmiiller space is the upper half-plane H (r G H parametrizes the lattice with generators { l , r } ) . rY/PSL (2;Z). e. the collection of real numbers which occur as lengths of closed geodesies) is discrete. Using this fact, one 30 3. Teichmuller Spaces and Mapping Class Groups can show, without much effort, that the action of the mapping class group T* on the Teichmuller space Tg is properly discontinuous, that is to say, that for every set K C Tg, the collection of $ £ TJ is such that, $ (K) fl K 7^ 0 , is finite.