402 research outputs found
On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for -Dynamical Systems
The analog of the Chern-Gauss-Bonnet theorem is studied for a -dynamical
system consisting of a -algebra equipped with an ergodic action of a
compact Lie group . The structure of the Lie algebra of
is used to interpret the Chevalley-Eilenberg complex with coefficients in the
smooth subalgebra as noncommutative differential forms
on the dynamical system. We conformally perturb the standard metric, which is
associated with the unique -invariant state on , by means of a Weyl
conformal factor given by a positive invertible element of the algebra, and
consider the Hermitian structure that it induces on the complex. A Hodge
decomposition theorem is proved, which allows us to relate the Euler
characteristic of the complex to the index properties of a Hodge-de Rham
operator for the perturbed metric. This operator, which is shown to be
selfadjoint, is a key ingredient in our construction of a spectral triple on
and a twisted spectral triple on its opposite algebra. The
conformal invariance of the Euler characteristic is interpreted as an
indication of the Chern-Gauss-Bonnet theorem in this setting. The spectral
triples encoding the conformally perturbed metrics are shown to enjoy the same
spectral summability properties as the unperturbed case
A twisted local index formula for curved noncommutative two tori
We consider the Dirac operator of a general metric in the canonical conformal
class on the noncommutative two torus, twisted by an idempotent (representing
the -theory class of a general noncommutative vector bundle), and derive a
local formula for the Fredholm index of the twisted Dirac operator. Our
approach is based on the McKean-Singer index formula, and explicit heat
expansion calculations by making use of Connes' pseudodifferential calculus. As
a technical tool, a new rearrangement lemma is proved to handle challenges
posed by the noncommutativity of the algebra and the presence of an idempotent
in the calculations in addition to a conformal factor.Comment: 27 page
تعیین ارتباط آپاندکتومی و سرطان روده بزرگ در بیماران مراجعه کننده به بیمارستان شهید باهنر و افضلی پور و مهرگان شهر کرمان در سال های ۹۵-۱۳۸۳
- …