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Knots and surfaces:

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Bibliographic Details
Main Authors:	Gilbert, N. D. (Author), Porter, Timothy (Author)
Format:	Book
Language:	English
Published:	Oxford [u.a.] Oxford Univ. Press 1995
Edition:	1. publ. in paperback
Series:	Oxford science publications
Subjects:	Knot theory Surfaces Knotentheorie Fläche
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 268 S. zahlr. graph. Darst.
ISBN:	0198514905

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MARC


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adam_text	KNOTS AND SURFACES N. D. GILBERT DEPARTMENT OF MATHEMATICS HERIOT-WATT UNIVERSITY, EDINBURGH T. PORTER SCHOOL OF MATHEMATICS, UNIVERSITY COLLEGE OF NORTH WALES, BANGOR OXFORD NEW YORK TOKYO OXFORD UNIVERSITY PRESS CONTENTS 1. KNOTS, LINKS, AND DIAGRAMS 1.1 KNOT AND LINK DIAGRAMS 1.2 ISOTOPY AND THE REIDEMEISTER MOVES 1.3 3-COLOURING 1.4 NUMERICAL INVARIANTS 1.5 CHIRAL AND INVERTIBLE KNOTS 2. KNOT AND LINK POLYNOMIALS 2.1 STATE MODEIS AND THE JONES POLYNOMIAL 2.2 THE JONES POLYNOMIAL 2.3 APPLICATIONS OF THE KAUFFMAN POLYNOMIAL 2.4 THE ORIENTED OR HOMFLY POLYNOMIAL 2.5 THE ALEXANDER POLYNOMIAL 3. TOPOLOGICAL SPACES 3.1 TOPOLOGICAL SPACES 3.2 CONTINUITY 3.3 CONNECTEDNESS 3.4 IDENTIFICATION SPACES 3.5 KNOTS AND ISOTOPY 4. SURFACES 4.1 COMBINATORIAL SURFACES 4.2 CUTTING AND PASTING 4.3 INVARIANTS OF SURFACES: ORIENTABILITY AND BOUNDARY CURVES 4.4 INVARIANTS OF SURFACES: EULER CHARACTERISTIC AND GENUS 4.5 KNOTS AND SURFACES 1 1 5 8 11 15 19 19 28 30 34 38 42 42 45 48 49 51 55 57 68 80 84 90 5. THE ARITHMETIC OF KNOTS 96 5.1 THE SUM OF ORIENTED KNOTS 96 5.2 GENUS OF K + L 100 X CONTENTS 5.3 BRIDGE NUMBER OF K + L 5.4 FACTORIZATIONS, PRIME KNOTS, AND THE FACTORIZATION THEOREM 5.5 N-COLOURABIHTY 5.6 POLYNOMIALS AND THE SUM OF KNOTS 6. PRESENTATIONS OF GROUPS 6.1 EXAMPLES OF PRESENTATIONS 6.2 DIHEDRAL GROUPS 6.3 CAYLEY QUIVERS 6.4 FREE GROUPS 6.5 PRESENTATIONS 6.6 TIETZE TRANSFORMATIONS 6.7 QUOTIENT GROUPS 6.8 ABELIANIZATION 6.9 FINITELY GENERATED ABELIAN GROUPS 6.10 PUSHOUTS OF GROUPS 6.11 KNOT GROUPS 7. GRAPHS AND TREES 7.1 GRAPHS, QUIVERS, AND TREES 7.2 EXAMPLES OF GRAPHS 7.3 PLANAR GRAPHS 7.4 EMBEDDING GRAPHS IN SURFACES 8. ALEXANDER MATRICES AND ALEXANDER POLYNOMIALS 8.1 GROUP RINGS 8.2 DERIVATIVES 8.3 THE ALEXANDER MATRIX 8.4 ELEMENTARY IDEALS 8.5 ALEXANDER POLYNOMIALS VIA THE WIRTINGER PRESENTATION 9. THE FUNDAMENTAL GROUP 9.1 PATHS 9.2 HOMOTOPY 9.3 CALCULATIONS OF THE FUNDAMENTAL GROUP 9.4 HOMOTOPY EQUIVALENCE 10. VAN KAMPEN S THEOREM 212 CONTENTS XI 11. APPLICATIONS OF THE VAN KAMPEN THEOREM 224 11.1 CALCULATIONS OF FUNDAMENTAL GROUPS 224 11.2 SURFACE GROUPS 233 11.3 SPACES WITH FINITE CYCLIC FUNDAMENTAL GROUP 236 11.4 SPACES WITH GIVEN FUNDAMENTAL GROUP 237 11.5 THE GROUP OF A KNOT 239 11.6 TORUS KNOTS 243 11.7 ANALYSIS OF THE KNOT GROUP G M * 246 12. COVERING SPACES 250 12.1 COVERING MAPS AND COVERING SPACES 250 12.2 DECK TRANSFORMATIONS AND UNIVERSAL COVERS 258 12.3 COVERING GRAPHS 259 BIBLIOGRAPHY 264 INDEX 266
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indexdate	2024-07-09T17:58:47Z
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isbn	0198514905
language	English
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physical	XI, 268 S. zahlr. graph. Darst.
publishDate	1995
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publisher	Oxford Univ. Press
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series2	Oxford science publications
spelling	Gilbert, N. D. Verfasser aut Knots and surfaces N. D. Gilbert ; T. Porter 1. publ. in paperback Oxford [u.a.] Oxford Univ. Press 1995 XI, 268 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Knot theory Surfaces Knotentheorie (DE-588)4164318-5 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Knotentheorie (DE-588)4164318-5 s Fläche (DE-588)4129864-0 s DE-604 Porter, Timothy Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007200922&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Gilbert, N. D. Porter, Timothy Knots and surfaces Knot theory Surfaces Knotentheorie (DE-588)4164318-5 gnd Fläche (DE-588)4129864-0 gnd
subject_GND	(DE-588)4164318-5 (DE-588)4129864-0
title	Knots and surfaces
title_auth	Knots and surfaces
title_exact_search	Knots and surfaces
title_full	Knots and surfaces N. D. Gilbert ; T. Porter
title_fullStr	Knots and surfaces N. D. Gilbert ; T. Porter
title_full_unstemmed	Knots and surfaces N. D. Gilbert ; T. Porter
title_short	Knots and surfaces
title_sort	knots and surfaces
topic	Knot theory Surfaces Knotentheorie (DE-588)4164318-5 gnd Fläche (DE-588)4129864-0 gnd
topic_facet	Knot theory Surfaces Knotentheorie Fläche
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