Rough index theory on spaces of polynomial growth and contractibility

DOI10.4171/JNCG/335zbMath1436.58019arXiv1505.03988WikidataQ127461708 ScholiaQ127461708MaRDI QIDQ2327774

Alexander Engel

Publication date: 15 October 2019

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.03988

zbMATH Keywords

Novikov conjectureuniform Roe algebrauniformly finite homology

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Index theory (19K56)

Related Items (11)

A quasi-local characterisation of \(L^{p}\)-Roe algebras ⋮ Quasi-locality for étale groupoids ⋮ Embeddings of von Neumann algebras into uniform Roe algebras and quasi-local algebras ⋮ Dynamic asymptotic dimension and Matui's HK conjecture ⋮ The strongly quasi-local coarse Novikov conjecture and Banach spaces with Property (H) ⋮ Width, largeness and index theory ⋮ Good Wannier bases in Hilbert modules associated to topological insulators ⋮ Relative commutant pictures of Roe algebras ⋮ Quasi-local algebras and asymptotic expanders ⋮ On the structure of asymptotic expanders ⋮ Quasi-locality and property A

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Wrong way maps in uniformly finite homology and homology of groups
• Algebraic \(K\)-theory and locally convex algebras
• Theory of function spaces
• Uniform \(K\)-homology theory
• An index theorem on open manifolds. I. II
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Hyperbolic metric spaces and the exotic cohomology Novikov conjecture
• Quotients of local Banach algebras are local Banach algebras
• Zero-in-the-spectrum conjecture, positive scalar curvature and asymptotic dimension
• Higher connectedness of asymptotic cones.
• Cyclic homology in non-commutative geometry
• Volume growth and positive scalar curvature
• Banach strong Novikov conjecture for polynomially contractible groups
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• Commutator structure of operator ideals
• Spectral invariant subalgebras of reduced crossed product \(C^*\)-algebras
• Cyclic cohomology and higher indices for noncompact complete manifolds
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces
• POLYNOMIAL DEHN FUNCTIONS AND THE LENGTH OF ASYNCHRONOUSLY AUTOMATIC STRUCTURES
• A SHORT PROOF THAT M_n(A) IS LOCAL IF A IS LOCAL AND FRÉCHET
• Aperiodic Tilings, Positive Scalar Curvature, and Amenability of Spaces
• Higher dimensional isoperimetric (or Dehn) functions of groups
• Equivalence of norms on operator space tensor products of $C^\ast $-algebras
• Coarse cohomology and index theory on complete Riemannian manifolds
• Codimension two index obstructions to positive scalar curvature

This page was built for publication: Rough index theory on spaces of polynomial growth and contractibility