Non-orientable surface-plus-one-relation groups

Details Non-orientable surface-plus-one-relation groups Non-orientable surface-plus-one-relation groups

2008-10-15

arxiv.org/abs/0810.2734v1

Journal of Algebra 326 (2011) 4-33

Mathematics

Group Theory

Version 1. 37 pages. 0 figures. Dedicated to the memory of Karl Gruenberg

Scientific paper

10.1016/j.jalgebra.2009.03.001

Recently Dicks-Linnell determined the $L^2$-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 $L^2$-Betti numbers of the non-orientable surface-plus-one-relation groups.

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