211 research outputs found
Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we
derive inequalities that involve a real parameter and join the eigenvalues of
the Dirac operator with curvature terms. The discussion of these inequalities
yields vanishing theorems for the kernel of the Dirac operator and lower
bounds for the spectrum of if the curvature satisfies certain conditions.Comment: Latex2e, 14p
Lower bounds for the first eigenvalue of the Dirac operator on compact Riemannian manifolds
AbstractSome new, improved, curvature depending lower bounds for the first eigenvalue of the Dirac operator on compact Riemannian manifolds are proved. If certain curvature conditions are satisfied, then these lower bounds are also useful in cases where the scalar curvature has zeros or attains negative values. This implies stronger vanishing theorems for harmonic spinors
From Linked Data to Relevant Data -- Time is the Essence
The Semantic Web initiative puts emphasis not primarily on putting data on
the Web, but rather on creating links in a way that both humans and machines
can explore the Web of data. When such users access the Web, they leave a trail
as Web servers maintain a history of requests. Web usage mining approaches have
been studied since the beginning of the Web given the log's huge potential for
purposes such as resource annotation, personalization, forecasting etc.
However, the impact of any such efforts has not really gone beyond generating
statistics detailing who, when, and how Web pages maintained by a Web server
were visited.Comment: 1st International Workshop on Usage Analysis and the Web of Data
(USEWOD2011) in the 20th International World Wide Web Conference (WWW2011),
Hyderabad, India, March 28th, 201
K\"ahlerian Twistor Spinors
On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural
analogue of twistor spinors on Riemannian spin manifolds. They are defined as
sections in the kernel of a first order differential operator adapted to the
K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study
K\"ahlerian twistor spinors and give a complete description of compact K\"ahler
manifolds of constant scalar curvature admitting such spinors. As in the
Riemannian case, the existence of K\"ahlerian twistor spinors is related to the
lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.
Relative commutants of strongly self-absorbing C*-algebras
The relative commutant of a strongly self-absorbing
algebra is indistinguishable from its ultrapower . This
applies both to the case when is the hyperfinite II factor and to the
case when it is a strongly self-absorbing C*-algebra. In the latter case we
prove analogous results for and reduced powers
corresponding to other filters on . Examples of algebras with
approximately inner flip and approximately inner half-flip are provided,
showing the optimality of our results. We also prove that strongly
self-absorbing algebras are smoothly classifiable, unlike the algebras with
approximately inner half-flip.Comment: Some minor correction
A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself
We give an example of an exact, stably finite, simple. separable C*-algebra D
which is not isomorphic to its opposite algebra. Moreover, D has the following
additional properties. It is stably finite, approximately divisible, has real
rank zero and stable rank one, has a unique tracial state, and the order on
projections over D is determined by traces. It also absorbs the Jiang-Su
algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also
explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard
order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such
an algebra has been moved to a separate paper (1309.4142 [math.OA]
Some integrability conditions for almost K\"ahler manifolds
Among other results, a compact almost K\"ahler manifold is proved to be
K\"ahler if the Ricci tensor is semi-negative and its length coincides with
that of the star Ricci tensor or if the Ricci tensor is semi-positive and its
first order covariant derivatives are Hermitian. Moreover, it is shown that
there are no compact almost K\"ahler manifolds with harmonic Weyl tensor and
non-parallel semi-positive Ricci tensor. Stronger results are obtained in
dimension 4.Comment: Latex2e, 13 page
Killing spinors in supergravity with 4-fluxes
We study the spinorial Killing equation of supergravity involving a torsion
3-form \T as well as a flux 4-form \F. In dimension seven, we construct
explicit families of compact solutions out of 3-Sasakian geometries, nearly
parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The
constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We
investigate the constraint \T \cdot \Psi = 0, too, and show that it singles
out a very special choice of numerical parameters in the Killing equation,
which can also be justified geometrically
C*-algebras associated with endomorphisms and polymorphisms of compact abelian groups
A surjective endomorphism or, more generally, a polymorphism in the sense of
\cite{SV}, of a compact abelian group induces a transformation of .
We study the C*-algebra generated by this operator together with the algebra of
continuous functions which acts as multiplication operators on .
Under a natural condition on the endo- or polymorphism, this algebra is simple
and can be described by generators and relations. In the case of an
endomorphism it is always purely infinite, while for a polymorphism in the
class we consider, it is either purely infinite or has a unique trace. We prove
a formula allowing to determine the -theory of these algebras and use it to
compute the -groups in a number of interesting examples.Comment: 25 page
- …