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Riemann, Topology, and Physics

  • Book
  • © 1999

Overview

Authors:
  1. Michael Monastyrsky

    1. Department of Theoretical Physics, Insitute for Theoretical and Experimental Physics, Moscow, Russia

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  • 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

Part of the book series: Modern Birkhäuser Classics (MBC)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xv
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  2. Bernhard Riemann

    1. Front Matter

      Pages 1-1
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    2. Beginnings

      • Michael Monastyrsky
      Pages 3-10

    3. Doctoral Dissertation

      • Michael Monastyrsky
      Pages 11-21

    4. Privatdozent at Göttingen

      • Michael Monastyrsky
      Pages 23-41

    5. Riemann and Dirichlet

      • Michael Monastyrsky
      Pages 43-62

    6. Full Professor in Göttingen

      • Michael Monastyrsky
      Pages 63-74

    7. Last Years

      • Michael Monastyrsky
      Pages 75-76

    8. Posthumous Fate

      • Michael Monastyrsky
      Pages 77-81

  3. Topological Themes in Contemporary Physics

    1. Front Matter

      Pages 85-87
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    2. Introduction

      • Michael Monastyrsky
      Pages 89-93

    3. Topological Structures

      • Michael Monastyrsky
      Pages 95-106

    4. The Connectivity of a Manifold and Quantization of Magnetic Flux

      • Michael Monastyrsky
      Pages 107-108

    5. Systems with Spontaneous Symmetry Breaking

      • Michael Monastyrsky
      Pages 109-112

    6. Topology and Liquid Crystals

      • Michael Monastyrsky
      Pages 113-126

    7. Theory of Gauge Fields

      • Michael Monastyrsky
      Pages 127-144

    8. Topological Particles

      • Michael Monastyrsky
      Pages 145-156

    9. Soliton Particles

      • Michael Monastyrsky
      Pages 157-166

    10. Knots, Links, and Physics

      • Michael Monastyrsky
      Pages 167-181

    11. What Next?

      • Michael Monastyrsky
      Pages 183-190
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Keywords

About this book

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.

Reviews

"This is a new translation of a book first published in English in 1987... Translated from Russian...it consists of two separate but related works. The first is an account of the life and work of Riemann, the second an account of several different topics in physics which are illuminated by the introduction of topological ideas. The discussion of Riemann is even better in the new edition. The mathematical account is richer and various errors have been corrected... The second half has been revised in a similar fashion... It has also been enriched by a new chapter which starts with von Neumann algebras and the work of Vaughn Jones... The book does three things very well: it reminds us of the range and depth of Riemann’s interests, which are emblematic of what the author values in mathematical physics; describes some of the many successes of Russian mathematicians and physicists; and it provides a lucid account of some modern work in which topology is genuinely applied. Books like this are vital for the health of mathematics and it is to be hoped that more will be written."

---Mathematical Reviews

"The book is highly recommendable—for students and scientific workers—not only for the valuable information in it, but also for its spirit: history and higher mathematics are not dry here; they become alive and motivate further studies."

---ZAA

Authors and Affiliations

  • Department of Theoretical Physics, Insitute for Theoretical and Experimental Physics, Moscow, Russia

    Michael Monastyrsky

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