5,372 research outputs found
Chern character for totally disconnected groups
No full textIn this paper we construct a bivariant Chern character for the equivariant -theory
of a totally disconnected group with values in bivariant equivariant cohomology in the sense of
Baum and Schneider. We prove in particular that the complexified left hand side of the Baum-Connes
conjecture for a totally disconnected group is isomorphic to cosheaf homology.
Moreover, it is shown that our transformation extends the Chern character defined by Baum and
Schneider for profinite groups
Symplectic Bott-Chern cohomology of solvmanifolds
No full textWe study the symplectic Bott-Chern cohomology by L.-S. Tseng and S.-T. Yau
for solvmanifolds endowed with left-invariant symplectic structures
Chern-flat and Ricci-flat invariant almost Hermitian structure
No full textWe study nilmanifolds endowed with a Chern connectio
Bott-Chern cohomology of solvmanifolds
No full textWe study conditions under which sub-complexes of a double complex of vector
spaces allow to compute the Bott-Chern cohomology. We are especially aimed at
studying the Bott-Chern cohomology of a special class of solvmanifolds
Quasi-Kahler Chern-flat manifolds and complex 2-step nilpotent Lie algebras
No full textThe study of quasi-Kaehler Chern-flat almost Hermitian manifolds is strictly related to the study of anti-bi-invariant almost complex Lie algebras. In the present paper we show that quasi-Kaehler Chern-flat almost Hermitian structures on compact manifolds are in correspondence to complex parallelisable Hermitian structures satisfying the second Gray identity. From an algebraic point of view this correspondence reads as a natural correspondence between anti-bi-invariant almost complex structures on Lie algebras to bi-invariant complex structures. Some natural algebraic problems are approached and some exotic examples are carefully describe
On the -Lemma and Bott-Chern cohomology
No full textOn a compact complex manifold X, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if X satisfies the ∂∂− -Lemma
Integral cohomology and chern classes of the special linear group over the ring of integers
No full textThis paper is devoted to the complete calculation of the additive structure of the 2-torsion of the integral cohomology of the innite special linear group SL(Z) over the ring of integers Z. This enables us to determine the best upper bound for the order of the Chern classes of all integral and rational representations of discrete groups.</p
Projective Dirac Operators, Twisted K-Theory, and Local Index Formula
No full textWe construct a canonical noncommutative spectral triple for every oriented closed Riemannian manifold, which represents the fundamental class in the twisted K-homology of the manifold. This so-called "projective spectral triple" is Morita equivalent to the well-known commutative spin spectral triple provided that the manifold is spin-c. We give an explicit local formula for the twisted Chern character for K-theories twisted with torsion classes, and with this formula we show that the twisted Chern character of the projective spectral triple is identical to the Poincare dual of the A-hat genus of the manifold
Chern-Simons supergravity on supergroup manifolds
No full textWe construct N=1 d=3 AdS supergravity within the group manifold approach and compare it with Achucarro-Townsend Chern-Simons formulation of the same theory. We clarify the relation between the off-shell super gauge transformations of the Chern- Simons theory and the off-shell worldvolume supersymmetry transformations of the group manifold action. We formulate the Achucarro-Townsend model in a double supersymmetric action where the Chern-Simons theory with a supergroup gauge symmetry is constructed on a supergroup manifold. This framework is useful to establish a correspondence of degrees of freedom and auxiliary fields between the two descriptions of d=3 supergravity
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