Warren Dicks, Peter A. Linnell
Abstract
We determine the L 2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L 2-cohomology of left-orderable groups, and deduce the non-L 2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.
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We determine the L 2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L 2-cohomology of left-orderable groups, and deduce the non-L 2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.
Key concepts: Mathematics, Betti number, Cohomology, Generator (circuit theory), Pure mathematics, Dimension (graph theory), Group (periodic table), Combinatorics