Abstract.
We consider the class of discrete groups which arise as fundamental groups of iterated surface fibrations; that is, of complexes obtained from a sequence of fibrations in which all bases and the initial fibre are hyperbolic surfaces. Group theoretically, this corresponds to studying the class of iterated extensions of hyperbolic surface groups. In [4], for the case of a single extension we conjectured and partially established that no group can arise from more than a finite number of such extensions. Here we show that the result holds in complete generality. As remarked in [4], the result has a strong affinity with the rigidity theorems of Parshin [7] and Arakelov [1] for fibred (complex) algebraic surfaces.
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Received: 1.5.1998
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Johnson, F. A rigidity theorem for group extensions. Arch. Math. 73, 81–89 (1999). https://doi.org/10.1007/s000130050371
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DOI: https://doi.org/10.1007/s000130050371