Riemann, Topology, and Physics

This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics.

Details a biography of one of the most important mathematicians in history, and an influential figure in the fields of philosophy and physics Great companion text to a history of geometry course

Klappentext

Ten years have passed since the publication of the first English edition. "Ten years is a long time, even when you are not in jail. " If we recall that the article on Riemann appeared in (Nature) in 1976, this Russian vaudeville joke is more than - propriate. Only the author's youth can account for the insane enterprise of presenting the scientific achievements and the biography of Riemann in 60 pages and the c- nection between physics and topology in the same space. Judging from the fact that the book sold out and got favorable reviews, there is a demand for publications of this type. It seems to me that popularizations aimed not at a narrow specialist but at a broader reader are especially needed nowadays. Specialists obtain information in their fields almost instantly thanks to the Internet, but to find out what is happening in contiguous fields, what problems and results are of great interest here, is not at all easy. Returning to my own book, I note with a certain pride that at least I seem to have evaluated accurately the trends in the development of theoretical physics. It is the combination of physics with topology and algebraic geometry that has led to the brightest achievements of mathematical physics in the last decade. It suffices to note the remarkable results of S.

Zusammenfassung
The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics.

Inhalt
Bernhard Riemann.- Beginnings.- Doctoral Dissertation.- Privatdozent at Göttingen.- Riemann and Dirichlet.- Full Professor in Göttingen.- Last Years.- Posthumous Fate.- Topological Themes in Contemporary Physics.- Topological Structures.- The Connectivity of a Manifold and Quantization of Magnetic Flux.- Systems with Spontaneous Symmetry Breaking.- Topology and Liquid Crystals.- Theory of Gauge Fields.- Topological Particles.- Soliton Particles.- Knots, Links, and Physics.- What Next?.- A Brief Historical Survey.