Knot Theory by Kurt Reidemeister

ISBN 0-914351-00-1 Order this book from BCS!

An English translation of Springer-Verlag's 1932 German edition.

Contents

1. Foreword to the English edition
2. Publisher's foreword to the original edition
3. Introduction
4. Chapter I: - Knots and their projections
   1. Definition of a knot
   2. Regular projections
   3. The operations \Omega. 1, 2, 3
   4. The subdivision of the projection plane into regions
   5. Normal knot projections
   6. Braids
   7. Knots and braids
   8. Parallel knots, Cable knots
5. Chapter II: - Knots and matrices
   1. Elementary invariants
   2. The matrices (c^h_{\alpha \beta})
   3. The matrix (a_i)
   4. The determinant of a knot
   5. The invariance of the trosion numbers
   6. The torsion numbers of particular knots
   7. The quadratic form of a knot
   8. Minkowski's units
   9. Minkowski's units for particular knots
   10. A determinant inequality
   11. Classification of alternating knots
   12. Almost alternating knots
   13. Almost alternating circles
   14. The L-polynomial of a knot
   15. L-polynomials of particular knots
6. Chapter III: - Knots and Groups
   1. Equivalence of braids
   2. The braid group
   3. Definition of the group of a knot
   4. Invariance of the knot group
   5. The group of the inverse knot and of the mirror image knot
   6. The matrix (l_ikx)) and the group
   7. The knot group and the matrices (c^h_{\alpha \beta})
   8. The edge path group of a knot
   9. Structure of the edge path group
   10. Covering spaces of the complementary space of the knot
   11. The group of a parallel knot
   12. The groups of torus knots
   13. The L-polynomials of parallel knots
   14. Several special knot groups
   15. A particular covering space
7. Table of knots
8. Bibliography
9. Index