Abstract:  Recently Dicks-Linnell determined the L²-Betti numbers of the orientable surface-plus-one-relation groups,
and their arguments involved some results that were obtained topologically by Hempel and Howie.
Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups,
and we then apply the extended results to determine the L²-Betti numbers of the non-orientable surface-plus-one-relation groups.

March 21, 2009 version, 40 pages, available as 368K Pdf file.

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