The Index of Operators on Foliated Bundles

نویسندگان

  • Victor Nistor
  • VICTOR NISTOR
چکیده

We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses techniques for analizing noncommutative algebras similar to those developed in Algebraic Topology, but in the framework of cyclic cohomology and noncommutative geometry.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cut-and-paste on Foliated Bundles

We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (≡ APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative index theorem for the difference of two APS-index classes associated to differe...

متن کامل

Index, Eta and Rho Invariants on Foliated Bundles

We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator Dm on the maximal Connes-Skandalis Hilbert module and explain how the functional calculus of Dm encodes both the leafwise calculus and the monodromy calculus in the corresponding von Neumann algebras. When the fol...

متن کامل

Homological index formulas for elliptic operators over C*-algebras

We prove index formulas for elliptic operators acting between spaces of sections of C∗-vector bundles on a closed manifold. The formulas involve Karoubi’s Chern character from K-theory of a C∗algebra to de Rham homology of smooth subalgebras. We show how they apply to the higher index theory for coverings and to flat foliated bundles, and prove an index theorem for C∗-dynamical systems associat...

متن کامل

3 J an 2 00 9 Homological index formulas for elliptic operators over C ∗ - algebras

We prove index formulas for elliptic operators acting between sections of C *-vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from K-theory of a C *-algebra to de Rham homology of smooth subalgebras. We show how they apply to the higher index theorem for coverings and to flat foliated bundles, and prove an index theorem for C *-dynamical systems associated to...

متن کامل

The Index of Hypoelliptic Operators on Foliated Manifolds

In [EE1] and [EE2] we presented the solution to the index problem for a natural class of hypoelliptic differential operators on compact contact manifolds. The methods developed to deal with that problem have wider applicability to the index theory of hypoelliptic Fredholm operators. As an example of the power of the proof techniques we present here a new proof of a little known index theorem of...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1996