Cohomology of 𝐹-groups

Curran, Peter

doi:10.1090/S0002-9947-1970-0272899-9

Cohomology of $F$-groups
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Trans. Amer. Math. Soc. 152 (1970), 609-621 Request permission

Abstract:

Let $G$ be a group of Möbius transformations and $V$ the space of complex polynomials of degree $\leqq$ some fixed even integer. Using the action of $G$ on $V$ defined by Eichler, we compute the dimension of the cohomology space ${H^1}(G,V)$, first for $G$ an arbitrary $F$-group (a generalization of Fuchsian group) and then for the free product of finitely many $F$-groups. These results extend those which Eichler obtained in a 1957 paper, where a correspondence was established between elements of ${H^1}(G,V)$ and cusp forms on $G$.

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