On the Equivalence of Geometric and Analytic K-Homology

Abstract

We give a proof that the geometric K-homology theory for finite CW-complexes defined by Baum and Douglas is isomorphic to Kasparov's K-homology. The proof is a simplification of more elaborate arguments which deal with the geometric formulation of equivariant K-homology theory.

29 pages, v4: corrected definition of E in proof of Prop 3.6

Cited by in corpus (36)

• Geometric quantization for proper actions
• The strong Novikov conjecture for low degree cohomology
• Differential K-theory. A survey
• Bivariant K-theory via correspondences
• Index, eta and rho-invariants on foliated bundles
• Dualities in equivariant Kasparov theory
• Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory
• Equivariant embedding theorems and topological index maps
• A Geometric Description of Equivariant K-Homology for Proper Actions
• The Real K-Theory of Compact Lie Groups
• Equivariant geometric K-homology for compact Lie group actions
• Positive Scalar Curvature and Poincare Duality for Proper Actions
• A noncommutative model for higher twisted K-Theory
• Riemann-Roch and index formulae in twisted K-theory
• Relative geometric assembly and mapping cones, Part I: The geometric model and applications
• Geometric K-homology with coefficients I
• The Higson-Roe exact sequence and ${\ell }^2$ eta invariants
• Equivariant twisted Real $K$-theory of compact Lie groups
• Realizing the analytic surgery group of Higson and Roe geometrically, Part II: Relative eta-invariants
• Codimension 2 transfer of higher index invariants
• Geometric cycles, index theory and twisted K-homology
• K-Theory, D-Branes and Ramond-Ramond Fields
• Log symplectic manifolds and $[Q,R]=0$
• KO-Homology and Type I String Theory
• The universal eta-invariant for manifolds with boundary
• A Dolbeault-Hilbert complex for a variety with isolated singular points
• On analytic Todd classes of singular varieties
• Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property
• Geometric and topological aspects of Type IIB D-branes
• Twisted K-homology,Geometric cycles and T-duality
• Induced character in equivariant K-theory and wreath products
• Index theory on the Miščenko bundle
• Orbifold index and equivariant K-homology
• An equivariant Poincaré duality for proper cocompact actions by matrix groups
• The Construction of Dirac Operators on Orientifolds
• Proper maps, bordism, and geometric quantization