Eta-invariants, torsion forms and flat vector bundles
نویسندگان
چکیده
We present a new proof, as well as a C/Q extension, of the RiemannRoch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The main techniques used are the computations of the adiabatic limits of ηinvariants associated to the so-called sub-signature operators. We further show that the Bismut-Lott analytic torsion form can be derived naturally from the transgression of the η-forms appearing in the adiabatic limit computations.
منابع مشابه
Absolute Torsion and Eta-invariant
In a recent joint work with V. Turaev [6], we defined a new concept of combinatorial torsion which we called absolute torsion. Compared with the classical Reidemeister torsion, it has the advantage of having a well-determined sign. Also, the absolute torsion is defined for arbitrary orientable flat vector bundles, and not only for unimodular ones, as is classical Reidemeister torsion. In this p...
متن کاملSecondary Analytic Indices
We define real-valued characteristic classes of flat complex vector bundles and flat real vector bundles with a duality structure. We construct pushforwards of such vector bundles with vanishing characteristic classes. These pushforwards involve the analytic torsion form in the first case and the eta-form of the signature operator in the second case. We show that the pushforwards are independen...
متن کاملDiffeomorphisms, Analytic Torsion and Noncommutative Geometry
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)).
متن کاملar X iv : d g - ga / 9 61 00 02 v 1 3 O ct 1 99 6 DETERMINANT LINES , VON NEUMANN ALGEBRAS AND L 2 TORSION
In this paper, we suggest a construction of determinant lines of finitely generated Hilbertian modules over finite von Neumann algebras. Nonzero elements of the determinant lines can be viewed as volume forms on the Hilbertian modules. Using this, we study both L combinatorial and L analytic torsion invariants associated to flat Hilbertian bundles over compact polyhedra and manifolds; we view t...
متن کاملJ an 2 00 3 MORSE THEORY AND HIGHER TORSION INVARIANTS
We compare the higher analytic torsion T of Bismut and Lott of a fibre bundle p:M → B equipped with a flat vector bundle F → M and a fibre-wise Morse function h on M with a higher torsion T that is constructed in terms of a families Thom-Smale complex associated to h and F , thereby extending previous joint work with Bismut. Under additional conditions on F , the torsion T is related to Igusa’s...
متن کامل