2000 character limit reached
Higher Kazhdan projections and delocalised $\ell^ 2$-Betti numbers (2405.03837v1)
Published 6 May 2024 in math.OA, math.GR, and math.KT
Abstract: We provide an explicit description of the K-classes of higher Kazhdan projections in degrees greater than 0 for specific free product groups and Cartesian product groups. Employing this description, we obtain new calculations of Lott's delocalised $\ell2$-Betti numbers. Notably, we establish the first non-vanishing results for infinite groups.
- A geometric description of equivariant K𝐾Kitalic_K-homology for proper actions. In Quanta of maths, volume 11 of Clay Math. Proc., pages 1–22. Amer. Math. Soc., Providence, RI, 2010.
- Cohomology of deformations. J. Topol. Anal., 7(1):81–104, 2015.
- Group algebra criteria for vanishing of cohomology. J. Funct. Anal., 279(11), 2020.
- L2subscript𝐿2L_{2}italic_L start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT-cohomology and group cohomology. Topology, 25:189–215, 1986.
- E. Brian Davies. One-parameter semigroups, volume 15 of Lond. Math. Soc. Monogr. Academic Press, London, 1980.
- Patrick Delorme. 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et resolubles. Produits tensoriels continus de représentations. Bull. Soc. Math. France, 105(3):281–336, 1977.
- The stable rank of some free product C∗superscript𝐶C^{*}italic_C start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT-algebras. Duke Math. J., 90(1):95–121, 1997.
- Vincent Lafforgue. K𝐾Kitalic_K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes. Invent. Math., 149(1):1–95, 2002.
- Higher Kazhdan projections, ℓ2superscriptℓ2\ell^{2}roman_ℓ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-Betti numbers and Baum-Connes conjectures. https://arxiv.org/abs/2006.09317, J. Noncommutative Geom., to appear, 2020.
- John Lott. Delocalized L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-invariants. J. Funct. Anal., 169(1):1–31, 1999.
- Michael Puschnigg. New holomorphically closed subalgebras of C∗superscript𝐶C^{*}italic_C start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT-algebras of hyperbolic groups. Geom. Funct. Anal., 20(1):243–259, 2010.
- Localized index and L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-Lefschetz fixed-point formula for orbifolds. J. Differential Geom., 102(2):285–349, 2016.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.