Bounded cohomology of certain groups of homeomorphisms

Abstract

We consider the condition when bounded cohomology injects into ordinary cohomology and prove the vanishing of bounded cohomology of the group of all compactly supported homeomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper R Superscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{{\mathbf {R}}^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

Locations

• Proceedings of the American Mathematical Society - View - PDF