Analytic K-Homology

By N. Higson, J. Roe. 2000

577 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/40944a2510c6ab1297f70266076c6447ba63e2cd

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Citations in the corpus

• Smoothness and Locality for Nonunital Spectral Triples (2003, methodology): “This is different to the usual definition of (locally) finite propagation speed for manifolds, [12], and is not uniform, in that M depends on m.”
• The noncommutative geometry of graph C*-algebras I: The index theorem (2005, methodology): “the positive spectral projection of 1 i d dθ . The pairing with idS1 is nontrivial on each summand, since φ(idS1) = S1 ···Sn ⊕ Pn i=2 ei,i is a unitary mapping p1Xpj to itself for each j. So we have, [16], idS1 × ψ∗φ ∗(X,P) = Xn j=1 Index(PidS1P: p1PXpj → p1PXpj) = − Xn j=1 (25) [pj] ∈ K0(Cn). By Pr”
• The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, background): “More informationaboutanalyticK-homologycanbe found inHigson– Roe [154].”
• K-Homology, Assembly and Rigidity Theorems for Relative Eta Invariants (2010, methodology): “We have used the term Dirac bundle to be consistent with the monograph [21]; the term Clifford bundle is used elsewhere.”
• Twisted K-Homology and Group-Valued Moment Maps (2010, methodology): “We will follow Kasparov’s approach [28, 29] towards K-homology of C∗-algebras, as described in Higson-Roe’s book [26].”
• Twisted K-theory (2004, methodology): “There does not seem to be an obvious map between the two groups, so we shall proceed indirectly, using Bott periodicity ([29],[8], [15]) for the Banach algebra Γ̂ formed by adjoining a unit to Γ = Γ(KP ).”
• C*-algebras associated with integral domains and crossed products by actions on adele spaces (2009, methodology): “Here, we take the product on K-theory as it is described in [HiRo], 4.”
• Some notes on Property A (2006, background): “See, for example, chapter 6 of [HR00b] or [Roe03], section 4.”