Lectures on the Topology of 3-Manifolds : : An Introduction to the Casson Invariant / / Nikolai Saveliev.
Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-sphe...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2011] ©2012 |
Year of Publication: | 2011 |
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Saveliev, Nikolai, author. aut http://id.loc.gov/vocabulary/relators/aut Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / Nikolai Saveliev. 2nd rev. ed. Berlin ; Boston : De Gruyter, [2011] ©2012 1 online resource (207 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook Frontmatter -- Preface -- Contents -- Introduction -- Glossary -- Lecture 1. Heegaard splittings -- Lecture 2. Dehn surgery -- Lecture 3. Kirby calculus -- Lecture 4. Even surgeries -- Lecture 5. Review of 4-manifolds -- Lecture 6. Four-manifolds with boundary -- Lecture 7. Invariants of knots and links -- Lecture 8. Fibered knots -- Lecture 9. The Arf-invariant -- Lecture 10. Rohlin’s theorem -- Lecture 11. The Rohlin invariant -- Lecture 12. The Casson invariant -- Lecture 13. The group SU(2) -- Lecture 14. Representation spaces -- Lecture 15. The local properties of representation spaces -- Lecture 16. Casson’s invariant for Heegaard splittings -- Lecture 17. Casson’s invariant for knots -- Lecture 18. An application of the Casson invariant -- Lecture 19. The Casson invariant of Seifert manifolds -- Conclusion -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The proof of the three-dimensional Poincaré conjecture has rendered this application moot but hardly made Casson's contribution less relevant: in fact, a lot of modern day topology, including a multitude of Floer homology theories, can be traced back to his λ-invariant. The principal goal of this book, now in its second revised edition, remains providing an introduction to the low-dimensional topology and Casson's theory; it also reaches out, when appropriate, to more recent research topics. The book covers some classical material, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It then proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and concludes with a brief overview of recent developments. The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincaré duality on manifolds. 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 29. Nov 2021) Casson invariant. Homology. Manifolds. Topology. MATHEMATICS / Geometry / Algebraic. bisacsh Casson. Invariant. Manifold. Saveliev, Nikolai, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb 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 2011 9783110261189 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011 9783110261233 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011 9783110261202 ZDB-23-DMN print 9783110250350 https://doi.org/10.1515/9783110250367 https://www.degruyter.com/isbn/9783110250367 Cover https://www.degruyter.com/document/cover/isbn/9783110250367/original |
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Saveliev, Nikolai, Saveliev, Nikolai, |
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Saveliev, Nikolai, Saveliev, Nikolai, Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / De Gruyter Textbook Frontmatter -- Preface -- Contents -- Introduction -- Glossary -- Lecture 1. Heegaard splittings -- Lecture 2. Dehn surgery -- Lecture 3. Kirby calculus -- Lecture 4. Even surgeries -- Lecture 5. Review of 4-manifolds -- Lecture 6. Four-manifolds with boundary -- Lecture 7. Invariants of knots and links -- Lecture 8. Fibered knots -- Lecture 9. The Arf-invariant -- Lecture 10. Rohlin’s theorem -- Lecture 11. The Rohlin invariant -- Lecture 12. The Casson invariant -- Lecture 13. The group SU(2) -- Lecture 14. Representation spaces -- Lecture 15. The local properties of representation spaces -- Lecture 16. Casson’s invariant for Heegaard splittings -- Lecture 17. Casson’s invariant for knots -- Lecture 18. An application of the Casson invariant -- Lecture 19. The Casson invariant of Seifert manifolds -- Conclusion -- Bibliography -- Index |
author_facet |
Saveliev, Nikolai, Saveliev, Nikolai, Saveliev, Nikolai, Saveliev, Nikolai, |
author_variant |
n s ns n s ns |
author_role |
VerfasserIn VerfasserIn |
author2 |
Saveliev, Nikolai, Saveliev, Nikolai, |
author2_variant |
n s ns n s ns |
author2_role |
MitwirkendeR MitwirkendeR |
author_sort |
Saveliev, Nikolai, |
title |
Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / |
title_sub |
An Introduction to the Casson Invariant / |
title_full |
Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / Nikolai Saveliev. |
title_fullStr |
Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / Nikolai Saveliev. |
title_full_unstemmed |
Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / Nikolai Saveliev. |
title_auth |
Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / |
title_alt |
Frontmatter -- Preface -- Contents -- Introduction -- Glossary -- Lecture 1. Heegaard splittings -- Lecture 2. Dehn surgery -- Lecture 3. Kirby calculus -- Lecture 4. Even surgeries -- Lecture 5. Review of 4-manifolds -- Lecture 6. Four-manifolds with boundary -- Lecture 7. Invariants of knots and links -- Lecture 8. Fibered knots -- Lecture 9. The Arf-invariant -- Lecture 10. Rohlin’s theorem -- Lecture 11. The Rohlin invariant -- Lecture 12. The Casson invariant -- Lecture 13. The group SU(2) -- Lecture 14. Representation spaces -- Lecture 15. The local properties of representation spaces -- Lecture 16. Casson’s invariant for Heegaard splittings -- Lecture 17. Casson’s invariant for knots -- Lecture 18. An application of the Casson invariant -- Lecture 19. The Casson invariant of Seifert manifolds -- Conclusion -- Bibliography -- Index |
title_new |
Lectures on the Topology of 3-Manifolds : |
title_sort |
lectures on the topology of 3-manifolds : an introduction to the casson invariant / |
series |
De Gruyter Textbook |
series2 |
De Gruyter Textbook |
publisher |
De Gruyter, |
publishDate |
2011 |
physical |
1 online resource (207 p.) |
edition |
2nd rev. ed. |
contents |
Frontmatter -- Preface -- Contents -- Introduction -- Glossary -- Lecture 1. Heegaard splittings -- Lecture 2. Dehn surgery -- Lecture 3. Kirby calculus -- Lecture 4. Even surgeries -- Lecture 5. Review of 4-manifolds -- Lecture 6. Four-manifolds with boundary -- Lecture 7. Invariants of knots and links -- Lecture 8. Fibered knots -- Lecture 9. The Arf-invariant -- Lecture 10. Rohlin’s theorem -- Lecture 11. The Rohlin invariant -- Lecture 12. The Casson invariant -- Lecture 13. The group SU(2) -- Lecture 14. Representation spaces -- Lecture 15. The local properties of representation spaces -- Lecture 16. Casson’s invariant for Heegaard splittings -- Lecture 17. Casson’s invariant for knots -- Lecture 18. An application of the Casson invariant -- Lecture 19. The Casson invariant of Seifert manifolds -- Conclusion -- Bibliography -- Index |
isbn |
9783110250367 9783110238570 9783110238471 9783110637205 9783110261189 9783110261233 9783110261202 9783110250350 |
url |
https://doi.org/10.1515/9783110250367 https://www.degruyter.com/isbn/9783110250367 https://www.degruyter.com/document/cover/isbn/9783110250367/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514.34 |
dewey-sort |
3514.34 |
dewey-raw |
514.34 |
dewey-search |
514.34 |
doi_str_mv |
10.1515/9783110250367 |
oclc_num |
979689603 |
work_keys_str_mv |
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status_str |
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ids_txt_mv |
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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 2011 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011 |
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Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant / |
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