Visual Geometry and Topology

  • Anatolij T. Fomenko

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Anatolij T. Fomenko
    Pages 1-73
  3. Anatolij T. Fomenko
    Pages 75-191
  4. Back Matter
    Pages 293-324

About this book

Introduction

Geometry and topology are strongly motivated by the visualization of ideal objects that have certain special characteristics. A clear formulation of a specific property or a logically consistent proof of a theorem often comes only after the mathematician has correctly "seen" what is going on. These pictures which are meant to serve as signposts leading to mathematical understanding, frequently also contain a beauty of their own. The principal aim of this book is to narrate, in an accessible and fairly visual language, about some classical and modern achievements of geometry and topology in both intrinsic mathematical problems and applications to mathematical physics. The book starts from classical notions of topology and ends with remarkable new results in Hamiltonian geometry. Fomenko lays special emphasis upon visual explanations of the problems and results and downplays the abstract logical aspects of calculations. As an example, readers can very quickly penetrate into the new theory of topological descriptions of integrable Hamiltonian differential equations. The book includes numerous graphical sheets drawn by the author, which are presented in special sections of "Visual material". These pictures illustrate the mathematical ideas and results contained in the book. Using these pictures, the reader can understand many modern mathematical ideas and methods. Although "Visual Geometry and Topology" is about mathematics, Fomenko has written and illustrated this book so that students and researchers from all the natural sciences and also artists and art students will find something of interest within its pages.

Keywords

Hamiltonian Systems Hamiltonsche Systeme Integrable Systems Integrierbare Systeme Visual Geometry Visual Topology Visuelle Geometrie Visuelle Topologie mathematical physics topology

Authors and affiliations

  • Anatolij T. Fomenko
    • 1
  1. 1.Dept. of Differential Geometry and Applications Faculty of Mathematics and MechanicsMoscow UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-76235-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-76237-6
  • Online ISBN 978-3-642-76235-2
  • About this book