Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20.50, 10.00

Retrieve articles in all journals with MSC: 20.50, 10.00


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0272899-9
Keywords: Cohomology space, $ F$-group, Fuchsian group, discontinuous group, cusp form
Article copyright: © Copyright 1970 American Mathematical Society