The equivariant Chern character and index of G-invariant operators. Lectures at CIME, Venise 1992

1993 ◽  
pp. 157-200 ◽  
Author(s):  
Nicole Berline ◽  
Michèle Vergne
Keyword(s):  
Chern Character

scholarly journals Higher spectral flow and an entire bivariant JLO cocycle

2012 ◽  
Vol 11 (1) ◽  
pp. 183-232 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
Alan L. Carey
Keyword(s):  
Dirac Operator ◽  
Chern Character ◽  
Dirac Operators ◽  
Cyclic Cohomology ◽  
Closed Manifold ◽  
Spectral Flow ◽  
Smooth Functions ◽  
Base Manifold ◽  
K Theory ◽  
Higher Spectral Flow

AbstractFor a single Dirac operator on a closed manifold the cocycle introduced by Jaffe-Lesniewski-Osterwalder [19] (abbreviated here to JLO), is a representative of Connes' Chern character map from the K-theory of the algebra of smooth functions on the manifold to its entire cyclic cohomology. Given a smooth fibration of closed manifolds and a family of generalized Dirac operators along the fibers, we define in this paper an associated bivariant JLO cocycle. We then prove that, for any l ≥ 0, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the Cl+1 topology and functions on the base manifold with the Cl topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

scholarly journals Chern character for twisted K-theory of orbifolds

2006 ◽  
Vol 207 (2) ◽  
pp. 455-483 ◽  
Author(s):  
Jean-Louis Tu ◽  
Ping Xu
Keyword(s):  
Chern Character ◽  
K Theory

scholarly journals On the Chern character of a theta-summable Fredholm module

1989 ◽  
Vol 84 (2) ◽  
pp. 343-357 ◽  
Author(s):  
Ezra Getzler ◽  
András Szenes
Keyword(s):  
Chern Character ◽  
Fredholm Module

K-theory of fine topological algebras, Chern character, and assembly

K-Theory ◽  
1992 ◽  
Vol 6 (1) ◽  
pp. 57-86 ◽  
Author(s):  
Ulrike Tillmann
Keyword(s):  
Chern Character ◽  
Topological Algebras ◽  
K Theory

scholarly journals Superconnections and the Chern character

Topology ◽  
1985 ◽  
Vol 24 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Daniel Quillen
Keyword(s):  
Chern Character

Loop spaces, cyclic homology and the Chern character

1989 ◽  
pp. 95-108
Author(s):  
E. Getzler ◽  
J.D.S. Jones ◽  
S.B. Petrack
Keyword(s):  
Chern Character ◽  
Cyclic Homology ◽  
Loop Spaces

scholarly journals Chern Character in Twisted K -Theory: Equivariant and Holomorphic Cases

2003 ◽  
Vol 236 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Varghese Mathai ◽  
Danny Stevenson
Keyword(s):  
Chern Character ◽  
K Theory

scholarly journals Chern characters, reduced ranks and -modules on the flag variety

1994 ◽  
Vol 37 (3) ◽  
pp. 477-482 ◽  
Author(s):  
T. J. Hodges ◽  
M. P. Holland
Keyword(s):  
Lie Algebra ◽  
Euler Characteristic ◽  
Maximal Ideal ◽  
Chern Character ◽  
Flag Variety ◽  
Central Character ◽  
Geometric Description ◽  
Semisimple Lie Algebra ◽  
Enveloping Algebra ◽  
Chern Characters

Let D be the factor of the enveloping algebra of a semisimple Lie algebra by its minimal primitive ideal with trival central character. We give a geometric description of the Chern character ch: K0(D)→HC0(D) and the state (of the maximal ideal m) s: K0(D)→K0(D/m) = ℤ in terms of the Euler characteristic χ:K0()→ℤ, where is the associated flag variety.

CHERN CHARACTER FOR DISCRETE GROUPS

1988 ◽  
pp. 163-232 ◽  
Author(s):  
Paul Baum ◽  
Alain Connes
Keyword(s):  
Chern Character ◽  
Discrete Groups

On the β-Construction in K-Theory

1972 ◽  
Vol 24 (5) ◽  
pp. 819-824
Author(s):  
C. M. Naylor
Keyword(s):  
Lie Group ◽  
Chern Character ◽  
Complex Representation ◽  
Group Homomorphism ◽  
Unique Element ◽  
Compact Lie Group ◽  
Fundamental Representation ◽  
K Theory ◽  
Simply Connected

The β-construction assigns to each complex representation φ of the compact Lie group G a unique element β(φ) in (G). For the details of this construction the reader is referred to [1] or [5]. The purpose of the present paper is to determine some of the properties of the element β(φ) in terms of the invariants of the representation φ. More precisely, we consider the following question. Let G be a simple, simply-connected compact Lie group and let f : S3 →G be a Lie group homomorphism. Then (S3) ⋍ Z with generator x = β(φ1), φ1 the fundamental representation of S3 , so that if φ is a representation of G,f*(φ) = n(φ)x, where n(φ) is an integer depending on φ and f . The problem is to determine n(φ).Since G is simple and simply-connected we may assume that ch2, the component of the Chern character in dimension 4 takes its values in H4(SG,Z)≅Z. Let u be a generator of H4(SG,Z) so that ch2(β (φ)) = m(φ)u, m(φ) an integer depending on φ.

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