2018/03/31 by Marc Bourdon, Bertrand Rémy, Bertrand Remy
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Artificial intelligence #Computer science #Geometric and Algebraic Topology #Mathematics #math.GR #msc:20J05 #msc:20J06 #msc:22E15 #msc:22E41 #msc:53C35 #msc:55B35 #msc:57T10 #msc:57T15
paper · pdf · doi:10.5802/ahl.61
published as Annales Henri Lebesgue, Volume 3 (2020) , pp. 1291-1326
openalex created_date 2018/04/06 · openalex publication_date 2020/11/05 · arxiv created 2021/01/18 · arxiv updated 2021/01/20 · openalex updated_date 2026/08/05
We show that the continuous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> -cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application, we prove partial results supporting a positive answer to a question asked by M. Gromov, suggesting a classical behaviour of continuous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> -cohomology of simple real Lie groups. In addition to quasi-isometric invariance, the ingredients are a spectral sequence argument and Pansu’s vanishing results for real hyperbolic spaces. In the best adapted cases of simple Lie groups, we obtain nearly half of the relevant vanishings.