Knots / / Gerhard Burde, Heiner Zieschang, Michael Heusener.
This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2013] ©2013 |
Year of Publication: | 2013 |
Edition: | 3rd fully revised and extended edition |
Language: | English |
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Physical Description: | 1 online resource (417 p.) |
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Burde, Gerhard, author. aut http://id.loc.gov/vocabulary/relators/aut Knots / Gerhard Burde, Heiner Zieschang, Michael Heusener. 3rd fully revised and extended edition Berlin ; Boston : De Gruyter, [2013] ©2013 1 online resource (417 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 5 Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Preface to the Third Edition -- Contents -- Chapter 1: Knots and isotopies -- Chapter 2: Geometric concepts -- Chapter 3: Knot groups -- Chapter 4: Commutator subgroup of a knot group -- Chapter 5: Fibered knots -- Chapter 6: A characterization of torus knots -- Chapter 7: Factorization of knots -- Chapter 8: Cyclic coverings and Alexander invariants -- Chapter 9: Free differential calculus and Alexander matrices -- Chapter 10: Braids -- Chapter 11: Manifolds as branched coverings -- Chapter 12: Montesinos links -- Chapter 13: Quadratic forms of a knot -- Chapter 14: Representations of knot groups -- Chapter 15: Knots, knot manifolds, and knot groups -- Chapter 16: Bridge number and companionship -- Chapter 17: The 2-variable skein polynomial -- Appendix A: Algebraic theorems -- Appendix B: Theorems of 3-dimensional topology -- Appendix C: Table -- Appendix D: Knot projections 01–949 -- References -- Author index -- Glossary of Symbols -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known. This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free differential calculus, braids, branched coverings and knots, Montesinos links, representations of knot groups, surgery of 3-manifolds and knots, Jones and HOMFLYPT polynomials. Knot theory has expanded enormously since the first edition of this book published in 1985. In this third completely revised and extended edition a chapter about bridge number and companionship of knots has been added. The book contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups, covering spaces and some basic results of combinatorial group theory are assumed to be known. The text is accessible to advanced undergraduate and graduate students in mathematics. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Knot theory. Knoten (Math.). MATHEMATICS / Geometry / General. bisacsh Alexander Polynomials. Braids. Branched Coverings. Cyclic Periods of Knots. Factorization. Fibred Knots. Homfly Polynomials. Knot Groups. Knots. Links. Montesinos Links. Seifert Matrices. Seifert Surface. Heusener, Michael, author. aut http://id.loc.gov/vocabulary/relators/aut Zieschang, Heiner, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013 9783110317350 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013 9783110317282 ZDB-23-DMI Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013 9783110317275 ZDB-23-DMP print 9783110270747 https://doi.org/10.1515/9783110270785 https://www.degruyter.com/isbn/9783110270785 Cover https://www.degruyter.com/document/cover/isbn/9783110270785/original |
language |
English |
format |
eBook |
author |
Burde, Gerhard, Burde, Gerhard, Heusener, Michael, Zieschang, Heiner, |
spellingShingle |
Burde, Gerhard, Burde, Gerhard, Heusener, Michael, Zieschang, Heiner, Knots / De Gruyter Studies in Mathematics , Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Preface to the Third Edition -- Contents -- Chapter 1: Knots and isotopies -- Chapter 2: Geometric concepts -- Chapter 3: Knot groups -- Chapter 4: Commutator subgroup of a knot group -- Chapter 5: Fibered knots -- Chapter 6: A characterization of torus knots -- Chapter 7: Factorization of knots -- Chapter 8: Cyclic coverings and Alexander invariants -- Chapter 9: Free differential calculus and Alexander matrices -- Chapter 10: Braids -- Chapter 11: Manifolds as branched coverings -- Chapter 12: Montesinos links -- Chapter 13: Quadratic forms of a knot -- Chapter 14: Representations of knot groups -- Chapter 15: Knots, knot manifolds, and knot groups -- Chapter 16: Bridge number and companionship -- Chapter 17: The 2-variable skein polynomial -- Appendix A: Algebraic theorems -- Appendix B: Theorems of 3-dimensional topology -- Appendix C: Table -- Appendix D: Knot projections 01–949 -- References -- Author index -- Glossary of Symbols -- Index |
author_facet |
Burde, Gerhard, Burde, Gerhard, Heusener, Michael, Zieschang, Heiner, Heusener, Michael, Heusener, Michael, Zieschang, Heiner, Zieschang, Heiner, |
author_variant |
g b gb g b gb m h mh h z hz |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Heusener, Michael, Heusener, Michael, Zieschang, Heiner, Zieschang, Heiner, |
author2_variant |
m h mh h z hz |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Burde, Gerhard, |
title |
Knots / |
title_full |
Knots / Gerhard Burde, Heiner Zieschang, Michael Heusener. |
title_fullStr |
Knots / Gerhard Burde, Heiner Zieschang, Michael Heusener. |
title_full_unstemmed |
Knots / Gerhard Burde, Heiner Zieschang, Michael Heusener. |
title_auth |
Knots / |
title_alt |
Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Preface to the Third Edition -- Contents -- Chapter 1: Knots and isotopies -- Chapter 2: Geometric concepts -- Chapter 3: Knot groups -- Chapter 4: Commutator subgroup of a knot group -- Chapter 5: Fibered knots -- Chapter 6: A characterization of torus knots -- Chapter 7: Factorization of knots -- Chapter 8: Cyclic coverings and Alexander invariants -- Chapter 9: Free differential calculus and Alexander matrices -- Chapter 10: Braids -- Chapter 11: Manifolds as branched coverings -- Chapter 12: Montesinos links -- Chapter 13: Quadratic forms of a knot -- Chapter 14: Representations of knot groups -- Chapter 15: Knots, knot manifolds, and knot groups -- Chapter 16: Bridge number and companionship -- Chapter 17: The 2-variable skein polynomial -- Appendix A: Algebraic theorems -- Appendix B: Theorems of 3-dimensional topology -- Appendix C: Table -- Appendix D: Knot projections 01–949 -- References -- Author index -- Glossary of Symbols -- Index |
title_new |
Knots / |
title_sort |
knots / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2013 |
physical |
1 online resource (417 p.) Issued also in print. |
edition |
3rd fully revised and extended edition |
contents |
Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Preface to the Third Edition -- Contents -- Chapter 1: Knots and isotopies -- Chapter 2: Geometric concepts -- Chapter 3: Knot groups -- Chapter 4: Commutator subgroup of a knot group -- Chapter 5: Fibered knots -- Chapter 6: A characterization of torus knots -- Chapter 7: Factorization of knots -- Chapter 8: Cyclic coverings and Alexander invariants -- Chapter 9: Free differential calculus and Alexander matrices -- Chapter 10: Braids -- Chapter 11: Manifolds as branched coverings -- Chapter 12: Montesinos links -- Chapter 13: Quadratic forms of a knot -- Chapter 14: Representations of knot groups -- Chapter 15: Knots, knot manifolds, and knot groups -- Chapter 16: Bridge number and companionship -- Chapter 17: The 2-variable skein polynomial -- Appendix A: Algebraic theorems -- Appendix B: Theorems of 3-dimensional topology -- Appendix C: Table -- Appendix D: Knot projections 01–949 -- References -- Author index -- Glossary of Symbols -- Index |
isbn |
9783110270785 9783110494938 9783110238570 9783110238471 9783110637205 9783110317350 9783110317282 9783110317275 9783110270747 |
issn |
0179-0986 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA612 |
callnumber-sort |
QA 3612.2 |
url |
https://doi.org/10.1515/9783110270785 https://www.degruyter.com/isbn/9783110270785 https://www.degruyter.com/document/cover/isbn/9783110270785/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514.2242 |
dewey-sort |
3514.2242 |
dewey-raw |
514.2242 |
dewey-search |
514.2242 |
doi_str_mv |
10.1515/9783110270785 |
oclc_num |
864432644 |
work_keys_str_mv |
AT burdegerhard knots AT heusenermichael knots AT zieschangheiner knots |
status_str |
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ids_txt_mv |
(DE-B1597)173980 (OCoLC)864432644 |
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Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013 Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013 Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013 |
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Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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The text is accessible to advanced undergraduate and graduate students in mathematics.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. 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