Non-orientable surface-plus-one-relation groups

Abstract

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.

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

References in corpus (2)

• L^2-Betti numbers of one-relator groups
• Retracts of vertex sets of trees and the almost stability theorem

Cited by in corpus (2)

• On the classifying space for proper actions of groups with cyclic torsion
• On the local-indicability Cohen-Lyndon Theorem