The bounded cohomology of SL_2 over local fields and S-integers
Michelle Bucher, Nicolas Monod
TL;DR
This paper proves that the continuous bounded cohomology of SL_2 over non-Archimedean local fields vanishes in all positive degrees, extending to boundary-transitive groups of tree automorphisms and S-integers.
Contribution
It establishes vanishing results for the bounded cohomology of SL_2 over certain fields and groups, generalizing previous knowledge in the area.
Findings
Bounded cohomology of SL_2 over non-Archimedean local fields vanishes in positive degrees.
Vanishing extends to boundary-transitive groups of tree automorphisms.
Low degree vanishing results for SL_2 over S-integers.
Abstract
It is proved that the continuous bounded cohomology of SL_2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for SL_2 over S-integers.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Algebra and Geometry · Advanced Operator Algebra Research