Stability results for Houghton groups

Abstract

We prove homological stability for a twisted version of the Houghton groups and their multidimensional analogues. Based on this, we can describe the homology of the Houghton groups and that of their multidimensional analogues over constant noetherian coefficients as an essentially finitely generated $FI$-module.

Added more detail in the proof of Propostion 1.12. Several other minor changes

References in corpus (2)

• FI-modules and stability for representations of symmetric groups
• FI-modules over Noetherian rings

Cited by in corpus (2)

• Homological stability of topological moduli spaces
• Central stability homology