Hearing the Platycosms

<I >Note by J.H. Conway.</I > The main result of the following paper is a proof of Rossetti’s theorem: {\it There is, up to scale, a unique isospectral pair of compact platycosms.} \noindent The proof follows Rossetti’s unpublished one (2001) almost exactly step by step –- my main contribution has been to shorten the exposition, chiefly by introducting conorms to make the argument more transparent, and by quoting Schiemann’s theorem, which Rossetti’s proof managed to avoid, except for the torocosm.

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Published 1 January 2006