# Books written by Sergei Novikov.

Novikov won the Fields Medal in 1970 for having made important advances in topology, the most well-known being his proof of the topological invariance of the Pontryagin classes of the differentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces.

## Modern Geometry ― Methods and Applications, Part I: The Geometry of Surfaces, Transformation Groups, and Fields

This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory.

## Modern Geometry― Methods and Applications, Part II: The Geometry and Topology of Manifolds

This is the second volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics.

## Modern Geometry―Methods and Applications, Part III: Introduction to Homology Theory

This is the third volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics.

## Topological Library, Part 1: Cobordisms and Their Applications

Series on Knots and Everything

## Topological Library, Part 2: Characteristic Classes and Smooth Structures on Manifolds

Series on Knots and Everything

## Modern Geometric Structures and Fields

The book presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the most important structures on them. The authors' approach is that the source of all constructions in Riemannian geometry is a manifold that allows one to compute scalar products of tangent vectors.

## Basic Elements of Differential Geometry and Topology

Mathematics and its Applications Book 60

## Solitons and Geometry

In this book, Professor Novikov describes recent developments in soliton theory and their relations to so-called Poisson geometry. This formalism, which is related to symplectic geometry, is extremely useful for the study of integrable systems that are described in terms of differential equations (ordinary or partial) and quantum field theories.

## Topology I: General Survey

The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present (1996) frontiers of research.

## Topology II: Homotopy and Homology, Classical Manifolds

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds.

## Elements of Mathematical Logic

## Dynamical Systems IV: Symplectic Geometry and its Applications

This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches.

## Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical Systems

A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.