E-theory and KK-theory for groups which act properly and isometrically on Hilbert space

By N. Higson, G. Kasparov. 2001

399 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/86227f9e63bdeb4bd0cabc7fc6c04eead3fb8be1

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ) (2006, neutral): “Primary 19K14, 46L35, 46L55, 46L80; Secondary”
On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup (2012, result): “es techniques that have been developed in connection with the Baum-Connes conjecture in [C-E-O], [E-L-P-W] and [Mey-Ne]. A combined statement of the relevant results is given in [E-N-O]. Note that by [H-K] all amenable groups (among many others) satisfy the Baum-Connes conjecture, so the results app”
K-Homology, Assembly and Rigidity Theorems for Relative Eta Invariants (2010, background): “The same holds more generally for torsion-free a-T-menable groups [13], and for these the Baum-Connes conjecture was proved in [20].”
Maximal and reduced Roe algebras of coarsely embeddable spaces (2011, methodology): “The techniques used are E-theoretic, building on work of Higson-Kasparov-Trout [12], [11] and Yu [28].”
The Haagerup property for locally compact quantum groups (2013, background): “Striking applications include Higson and Kasparov’s proof of the Baum–Connes conjecture in the presence of the Haagerup property [40], and Popa’s deformation-rigidity approach to structural properties of type II1 factors [62, 63].”
Isometric Group Actions on Banach Spaces and Representations Vanishing at Infinity (2006, background): “hand, a group is said to be a-T-menable if it admits a metrically proper ane action on a Hilbert space, and a deep result of Higson and Kasparov [ HiKa ] asserts that an a-T-menable group satises the Baum{Connes conjecture.”
Some geometric groups with Rapid Decay (2003, methodology): “†† Partially supported by Tufts University FRAC award.”
The coarse geometric Novikov conjecture and uniform convexity (2005, methodology): “The proof of the Hilbert space case makes the use of an algebra of the Hilbert space introduced in [21] [22] [23].”
The Novikov Conjecture for Linear Groups (2005, background): “Indeed we show that a group Γ as in the statement admits a metrically proper, isometric action on a Hilbert space (Higson and Kasparov showed in [19] [20] that if Γ is a group which admits such an action then the Baum- Connes assembly map (1) is an isomorphism for any A).”
Actions of Picture Groups on CAT(0) Cubical Complexes (2005, neutral): “One important reason was given by Higson and Kasparov [15], who showed that every discrete a-T-menable group satisfies the”
The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, methodology): “We already mentioned that Higson–Kasparov [149] treat second countable locally compact topological groups.”
Permanence properties of the Baum-Connes conjecture (2001, background): “Moreover, by the work of Kasparov, [15] [14], every group which can be embedded as a closed subgroup of an almost connected group (i.e., a group with compact component group G/G 0 ) has a γ-element.”
Hyperbolic groups admit proper affine isometric actions on lp-spaces (2004, methodology): “This result has important applications to K-theory of group C-algebras [13] [14].”
Groups acting properly on “bolic” spaces and the Novikov conjecture (2003, methodology): “The dual Dirac construction for euclidean spaces ([HKT], [ HK ])”
Proper isometric actions of Thompson's groups on Hilbert space (2003, background): “IMRN International Mathematics Research Notices 2003, No. 45 Proper Isometric Actions of Thompson’s Groups on Hilbert Space Daniel S. Farley”