On the Equivalence of Geometric and Analytic K-Homology

By P. Baum, N. Higson, Thomas Schick. 2007

100 citations recorded by the source corpus.

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

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0815c338873c5afda0dad0c59086b8c98c412a91

How researchers see this paper

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In Computational Theory and Mathematics

1. Guoliang Yu
2. J. Roe
3. Rufus Willett
4. U. Bunke
5. N. Higson
6. Thomas Schick

In Mathematical Physics

1. Rufus Willett
2. Guoliang Yu
3. Thomas Schick
4. J. Roe
5. N. Higson
6. U. Bunke
7. E. Guentner
8. Nathanial P. Brown Narutaka Ozawa

Citations in the corpus

• Higher index theory for certain expanders and Gromov monster groups I (2010, methodology): “Using the Baum–Douglas geometric model of K-homology as recently studied by Baum–Higson–Schick [7], [x] can be represented by a cycle (M,E, f) whereM is a compact spin manifold, E is a complex vector bundle overM , and f : M → Y is a continuous map.”
• SMOOTH K-THEORY (2007, background): “he Spinc-cobordism theory, and β is the homological Chern character. We consider all groups as Z/2Z-graded. The homological Chern character is a rational isomorphism. Furthermore one knows by [BD82], [BHS] that ΩSpinc ∗ (B) →α K ∗(B) is surjective. It follows that the composition β ◦α : ΩSpinc(B)⊗ Q”
• K-Homology, Assembly and Rigidity Theorems for Relative Eta Invariants (2010, methodology): “They may be concretely defined using either functional analysis [25, 12] (as first suggested by Atiyah [1]) or geometry [8, 10].”