Braids and Coverings Selected Topics [Hardcover]

Essays develop the elementary theory of Artin Braid groups geometrically and via homotopy theory, discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem and investigate polynomial covering maps.Essays develop the elementary theory of Artin Braid groups geometrically and via homotopy theory, discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem and investigate polynomial covering maps.This book is based on a graduate course taught by the author at the University of Maryland. The lecture notes have been revised and augmented by examples. The first two chapters develop the elementary theory of Artin Braid groups, both geometrically and via homotopy theory, and discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem. The final two chapters give a detailed investigation of polynomial covering maps, which may be viewed as a homomorphism of the fundamental group of the base space into the Artin Braid group on n strings.Preface; 1. Braids and configuration spaces; 2. Braids and links; 3. Polynomial covering maps; 4. Algebra and topology of Weierstrass polynomials; Appendces; Bibliography; Index. ...a good source for a one-semester topics course for graduate students with basic experience in topology....Each chapter of the book contains well-selected problems, which makes it even more valuable for work with students. To sum up, the book is a very good addition to the literature. Serge L. Tabachnikov, Mathematical Reviews