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On the cohomology of Fuchsian groups. (Chinese. English summary) Zbl 0903.30031
In this paper the following theorem is shown: If $$\Gamma$$ is a Fuchsian group and $$G$$ is the $$Z\Gamma$$-module, then $$H^i(\Gamma,G)\approx \oplus_{\Theta}\ker (G_\theta\to G^\theta)$$ as $$i$$ is an odd number $$>1$$ and $$H^i(\Gamma, G)\approx\oplus_\Theta G^\theta/NG$$ as $$i$$ is an even number $$>2$$.
Reviewer: Li Zhong (Beijing)
MSC:
 30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
Keywords:
Fuchsian groups; $$Z\Gamma$$-module