Braids and Coverings : Selected Topics
Vagn Lundsgaard. Hansen
Bok Engelsk 1989 · Electronic books.
| Annen tittel | |
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| Medvirkende | Series, C. M (Contributor)
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| Utgitt | Cambridge : Cambridge University Press , 1989
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| Omfang | 1 online resource (203 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Title; Copyright; Dedication; Preface; Preface; Contents; Contents; Chapter I. BRAIDS AND CONFIGURATION SPACES.; 1. Geometric braids; 2. Configuration spaces of ordered finite pointsets andtheir fibrations; 3. The braid group as fundamental group of aconfiguration space; 4. Artin's presentation of the braid group; 5. Representation of braids as automorphisms of free groups; 6. The Dirac string problem; Exercises; Chapter II. BRAIDS AND LINKS.; 1. Constructing links from braids; 2. Representing link types by closed braids.A theorem of Alexander. - 3. Combinatorial equivalence of closed braids.Markov's theorem4. The group of a link; 5. Plane projections and braid representations of links; Exercises; Chapter III. POLYNOMIAL COVERING MAPS.; 1. Weierstrass polynomials and the finite covering mapsassociated with them; 2. The canonical n-fold polynomial covering map; 3. Geometric characterizations of polynomial covering maps; 4. Polynomial covering maps and homomorphisms into braid groups; 5. Characteristic homomorphisms for finite covering maps; 6. An algebraic classification of the polynomial covering maps. - 7. Embedding finite covering maps into bundles of manifoldsExercises; Chapter IV. ALGEBRA AND TOPOLOGY OFWEIERSTRASS POLYNOMIALS.; 1. Complete solvability of equations defined by simpleWeierstrass polynomials; 2. Primitives for extensions of rings of continuous functions; 3. The characteristic algebra of a finite covering map; 4. Weierstrass polynomials and characteristic algebras; 5. Some applications of characteristic algebras; Exercises; Appendix 1: A presentation for the abstract coloured braid group; Appendix 2: Threading knot diagrams; Bibliography; Index. - This book is based on a graduate course taught by the author at the University of Maryland, USA. The lecture notes have been revised and augmented by examples. The work falls into two strands. 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 Markov'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
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 0521384796. - 0521387574
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