Subfactors and Knots Expository Lectures
Regional Conference
Seiten
1991
American Mathematical Society (Verlag)
978-0-8218-0729-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-0729-3 (ISBN)
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Presents an introduction to the theory of von Neumann algebras and to knot theory and braid groups. This book covers the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results.
This book is based on a set of lectures presented by the author at the NSF-CBMS Regional Conference, Applications of Operator Algebras to Knot Theory and Mathematical Physics, held at the U.S. Naval Academy in Annapolis in June 1988. The audience consisted of low-dimensional topologists and operator algebraists, so the speaker attempted to make the material comprehensible to both groups. He provides an extensive introduction to the theory of von Neumann algebras and to knot theory and braid groups.The presentation follows the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results. The author treats in detail the Homfly and Kauffman polynomials, introduces statistical mechanical methods on knot diagrams, and attempts an analogy with conformal field theory. Written by one of the foremost mathematicians of the day, this book will give readers an appreciation of the unexpected interconnections between different parts of mathematics and physics.
This book is based on a set of lectures presented by the author at the NSF-CBMS Regional Conference, Applications of Operator Algebras to Knot Theory and Mathematical Physics, held at the U.S. Naval Academy in Annapolis in June 1988. The audience consisted of low-dimensional topologists and operator algebraists, so the speaker attempted to make the material comprehensible to both groups. He provides an extensive introduction to the theory of von Neumann algebras and to knot theory and braid groups.The presentation follows the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results. The author treats in detail the Homfly and Kauffman polynomials, introduces statistical mechanical methods on knot diagrams, and attempts an analogy with conformal field theory. Written by one of the foremost mathematicians of the day, this book will give readers an appreciation of the unexpected interconnections between different parts of mathematics and physics.
von Neumann algebras Group actions and subfactors Values of the index, Virasoro algebra Construction of examples, further structure The braid group and its representations Knots and links The knot polynomial $V_L$ Knots and statistical mechanics The algebraic approach.
Erscheint lt. Verlag | 30.11.1991 |
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Reihe/Serie | CBMS Regional Conference Series in Mathematics |
Verlagsort | Providence |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-8218-0729-3 / 0821807293 |
ISBN-13 | 978-0-8218-0729-3 / 9780821807293 |
Zustand | Neuware |
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