UID:
almahu_9949462114802882
Format:
1 online resource (207 p.)
Edition:
2nd rev. ed.
ISBN:
9783110250367
,
9783110238570
Series Statement:
De Gruyter Textbook
Content:
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.
Note:
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
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202
Additional Edition:
ISBN 9783110250350
Language:
English
DOI:
10.1515/9783110250367
URL:
https://doi.org/10.1515/9783110250367
URL:
https://www.degruyter.com/isbn/9783110250367
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