Diffeomorphisms, Analytic Torsion and Noncommutative Geometry
نویسنده
چکیده
We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct an associated analytic torsion form T . If Z is a smooth closed aspherical manifold, we show that T gives invariants of π∗(Diff(Z)).
منابع مشابه
Nonholonomic Clifford Structures and Noncommutative Riemann–Finsler Geometry
We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann– Cartan space) defined by a generic off–diagonal metric structure (with an additional affine connection possessing nontrivial torsi...
متن کاملNoncommutative Geometry of the h-deformed Quantum Plane
The h-deformed quantum plane is a counterpart of the q-deformed one in the set of quantum planes which are covariant under those quantum deformations of GL(2) which admit a central determinant. We have investigated the noncommutative geometry of the h-deformed quantum plane. There is a 2-parameter family of torsion-free linear connections, a 1-parameter sub-family of which are compatible with a...
متن کاملar X iv : h ep - t h / 94 11 12 7 v 2 1 9 D ec 1 99 4 Linear Connections on Matrix Geometries
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection. 1 Introduction and Motivation The extension to noncommutative algebras of the notion of a differential calculus has been given both without (C...
متن کاملGeometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
A detailed description of the infinite-dimensional Lie algebra of ⋆-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C∗-algebra of compact o...
متن کاملRepresentations of the Weyl Algebra in Quantum Geometry
The Weyl algebra A of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of A having a cyclic and diffeomorphism invariant vector, is already unitarily equivalent to the fundamental representation. Additional assumptions concern the dimen...
متن کامل