The book presents a class of new results in molecular biology for which topological methods and ideas are important. hese include the large-scale conformation properties of DNA, computational methods (Monte Carlo) allowing the simulation of large-scale properties of DNA, the tangle model of DNA recombination and other applications of Knot theory, dynamics of supercoiled DNA and biocatalitic properties of DNA, the structure of proteins, and other very recent problems in molecular biology. The text also provides a short course of modern topology intended for the broad audience of biologists and physicists. The authors are renowned specialists in their fields and some of the new results presented here are documented for the first time in monographic form.

1. Introduction

2. Topology in Biology: From DNA Mechanics to Enzymology
3. Monte Carlo Simulation of DNA Topological Properties
4. Dynamics of DNA Supercoiling
5. From Tangle Fractions to DNA
6. Linear Behavior of the Writhe Versus the Number of Crossings in Rational Knots and Links
7. Combinatories and Topology of the ß-Sandwich and ß-Barrel Proteins
8. The Structure of Collagen. 9. Euler Charactristic, Dehn-Sommerville Characteristics, and their Applications
10. Hopf Fibration and its Applications
11. Multivalued Functionals, One-forms and Deformed de Rham Complex
12. The Spectral Geometry of Riemann Surfaces.