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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cohomology of $ F$-groups

Author: Peter Curran
Journal: Trans. Amer. Math. Soc. 152 (1970), 609-621
MSC: Primary 20.50; Secondary 10.00
MathSciNet review: 0272899
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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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Keywords: Cohomology space, $ F$-group, Fuchsian group, discontinuous group, cusp form
Article copyright: © Copyright 1970 American Mathematical Society