The first edition of this book presented simple proofs of the Atiyah-Singer Index Theorem for
Dirac operators on compact Riemannian manifolds and its generalizations (due to the …

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a
local formula for the index of any elliptic complex. Heat equation methods are also used to …

Let i: Y—> X be an embedding of compact complex manifolds. Let r| be a holomorphic vector
bundle on Y and let (0.1)(^): o^-^ _,...-^-. 0 vv be a holomorphic chain complex of vector …

There is the general principle to consider a classical invariant of a closed Riemannian
manifold M and to define its analog for the universal covering M taking the action of the …

We prove in this paper an arithmetic analog of the Riemann-Roch-Grothendieck theorem for
the determinant of the cohomology of an Hermitian vector bundle of arbitrary rank on a …

The two-loop contribution to the type IIB low energy effective action term D4R4, predicted by
SL (2, Z) duality, is compared with that of the two-loop 4-point function derived recently in …

The present book is a new revised and updated version of “Number Theory I. Introduction to
Number Theory” by Yu. I. Manin and AA Panchishkin, appeared in 1989 in Moscow (VINITI …

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The
proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise …

The purpose of this paper is to construct Quillen metrics on the equivariant determinant of
the cohomology of a holomorphic vector bundle with respect to the action of a compact …

To a flat vector bundle, one can associate odd real characteristic classes. Bismut and Lott
have proved a Riemann-Roch-Grothendieck theorem for such classes, when taking the …