Visual Geometry and Topology

Translator: Tsaplina, M.V.
The principal aim of this treatise is to explore classical and modern achievements of geometry and topology in both intrinsic mathematical problems and applications to mathematical physics. It describes specifically new results in Hamiltonian geometry.

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Geometry and topology are strongly motivated by the visualization of ideal objects that have certain special characteristics. The principal aim of this book is to narrate, in an accessible and fairly visual language, 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 new results in Hamiltonian geometry. The author gives visual explanations of the problems and results, without recourse to the abstract logical aspects of calculations. The book includes numerous graphical sheets drawn by the author, which illustrate the mathematical ideas and results contained in the book. Using these pictures, the reader can understand many modern mathematical ideas and methods.