Knots, braids and Möbius strips. Particle physics and the geometry of elementarity: an alternative view (Q2799470)

The \textit{Series on Knots and Everything} edited by Louis Kauffman from the University of Illinois have one major purpose: to explore the relations of physics, mathematics, logic, linguistics, philosophy and biology with knot theory. Volume 1 in this series written by Kauffman has the title \textit{Knots and Physics}. Many further volumes continue this enterprise with new and separate ideas. Volume 55 written by Jack Avrin provides an alternative view to elementary particle physics and the underlying geometry. To make sure, this book is not a first course in mathematical physics but rather a discussion, abundant in words, of history and philosophy in connection with physical and geometric concepts. Avrin declares: ``In fact, I'm not a physicist at all. Nor a mathematician.'' The book has seven sections. The main purpose of Section I is an introduction into some history and philosophy. Leaving this realm, Section II discusses basic concepts of algebraic geometry. In Section III, the author takes some time to look at several algebraic themes that are not part of the main line. Section IV makes the comparison between the developments in Section I and II and the Standard Model of particle physics. Section V discusses the role of differential geometry in particle physics. Section VI is devoted to a variety of topics not particularly related to previous sections, among them dark matter and string theory. Finally, Section VII is intended to recapitulate what has been discussed before and then presents current views of cosmology in a rather personal manner, in particular, a speculative connection between knots and the cosmos. The seven sections of this monograph give a broad, user-friendly introduction to the algebraic and geometric program in physics and beyond.