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Keywords
(2)
cyclic cohomology
Hyperbolic Group
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Cyclic cohomology, the Novikov conjecture and hyperbolic groups
Cyclic cohomology, the Novikov conjecture and hyperbolic groups,10.1016/00409383(90)900033,Topology,A Connes
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Cyclic cohomology, the Novikov conjecture and hyperbolic groups
(
Citations: 156
)
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A Connes
Journal:
Topology
, vol. 29, no. 3, pp. 345388, 1990
DOI:
10.1016/00409383(90)900033
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Citation Context
(83)
...Let D be an elliptic differential operator on a compact manifold M. As is wellknown ellipticity implies that D is a Fredholm operator and the AtiyahSinger index theorem [ATSI] expresses the index of D as a topological formula involving the Chern character of the symbol s(D) and the Todd class of the manifold M. In [
COMO
], CONNES–MOSCOVICI proved a far reaching generalization of the Atiyah–Singer index theorem, the socalled higher index ...
...the pairing ind[f ](D) = h X[f ],Ch(eD)i . The higher index theorem in [
COMO
] computes this number  which no longer is integral  in terms of topological data generalizing the Atiyah–Singer index theorem...
...rive CONNES–MOSCOVICI’s higher index from the higher algebraic index theorem, we prove that the algebraic pairing h Q(a), P1 − P2i coincides asymptotically with the pairing h X[f ],Ch(eD)i defined in [
COMO
]...
...Recall that CONNES–MOSCOVICI [
COMO
] used their higher index theorem to prove a covering index theorem, which was used to prove the Novikov conjecture...
...CONNES–MOSCOVICI defined in [
COMO
, §2.]...
...First, the map ¶ : K1 C ¥(S∗Q) � → K0 YDO−¥(Q) � is the index map (cf. [
COMO
,...
...Let us explain, why the definition of the localized index by Eq. 6.19 coincides with the original definition by [
COMO
]...
...[
COMO
, p. 353], and that this operator is homotopic to the graph projection of D (cf...
...Hereby,V1 −V2 is the virtual vector bundle obtained by the asymptotic limit ¯h ց 0 of r. We have thus reproved the following result from [
COMO
]...
M. J. Pflaum
,
et al.
Cyclic cocycles on deformation quantizations and higher index theorems
...and one wishes to calculate the diagonal map �. From cyclic cohomology invariants of B one thus gets Ktheory invariants of A ; this is used for instance in the formulation of higher index theorems [
6
]...
Denis Perrot
.
Quasihomomorphisms and the residue Chern character
...For the conjugacy class of the unit this result is due to Connes and Moscovici [
CM
] and plays a crucial role in their proof of the Novikov higher signature conjecture for wordhyperbolic groups...
...nents. On the other hand the closure of the subcomplex CChei( l C) corresponding to the conjugacy class of the unit element denes a direct topological summand of the analytic cyclic bicomplex of any unconditional admissible Fr echet algebra over l C. This was observed by Connes and Moscovici in [
CM
] and plays a crucial role in their proof of the Novikov higher signature conjecture for wordhyperbolic groups...
...Proof: Using the ideas of [
CM
], this is an immediate consequence of 6.3...
Michael Puschnigg
.
New Holomorphically Closed Subalgebras of C* Algebras of Hyperbolic G...
...In [40] D. Tamarkin and B. Tsygan, inspired by the ConnesMoscovici higher index formulas [
14
], suggested the rst version of the algebraic index theorem for a Poisson manifold...
V. A. Dolgushev
,
et al.
An algebraic index theorem for Poisson manifolds
...One of the main motivations to study the index theory of Dirac operator twisted by C ∗vector bundles comes from higher index theory, pioneered by ConnesMoscovici with their higher index theorem and relevant in connection with the Novikov conjecture [
CM
]...
...r. An appropriate system of Banach algebras can be gained fro m the work of ConnesMoscovici [
CM
]...
...In the following let A = C ∗. We assume that the projective system ( Ai)i∈IN0 is such that C ⊂ A∞. For the reduced group C ∗algebra C ∗ r a suitable projective system of algebras (Bi)i∈IN can be derived from a construction of Connes–Moscovici [
CM
], see for example [W2, §4] for a detailed account...
Charlotte Wahl
.
The AtiyahPatodiSinger index theorem for Dirac operators over C*alg...
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Citations
(156)
Eta cocycles, relative pairings and the GodbillonVey index theorem
Hitoshi Moriyoshi
,
Paolo Piazza
Published in 2011.
The ChernConnes character is not rationally injective
Michael Puschnigg
Published in 2011.
Cyclic cocycles on deformation quantizations and higher index theorems
(
Citations: 2
)
M. J. Pflaum
,
H. Posthuma
,
X. Tang
Journal:
Advances in Mathematics  ADVAN MATH
, vol. 223, no. 6, pp. 19582021, 2010
Quasihomomorphisms and the residue Chern character
(
Citations: 1
)
Denis Perrot
Journal:
Journal of Geometry and Physics  J GEOM PHYSICS
, vol. 60, no. 10, pp. 14411473, 2010
Compact $\kappa$deformation and spectral triples
Bruno Iochum
,
Thierry Masson
,
Thomas Schücker
,
Andrzej Sitarz
Published in 2010.