Circle-valued Morse Theory / / Andrei V. Pajitnov.
In the early 1920s M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. Circle-valued Morse theory o...
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Pajitnov, Andrei V., author. aut http://id.loc.gov/vocabulary/relators/aut Circle-valued Morse Theory / Andrei V. Pajitnov. Berlin ; Boston : De Gruyter, [2008] ©2006 1 online resource (454 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 32 Frontmatter -- Contents -- Preface -- Introduction -- Part 1. Morse functions and vector fields on -- manifolds -- CHAPTER 1. Vector fields and C0 topology -- CHAPTER 2. Morse functions and their -- gradients -- CHAPTER 3. Gradient flows of real-valued Morse -- functions -- Part 2. Transversality, handles, Morse -- complexes -- CHAPTER 4. The Kupka-Smale transversality theory -- for gradient flows -- CHAPTER 5. Handles -- CHAPTER 6. The Morse complex of a Morse -- function -- Part 3. Cellular gradients -- CHAPTER 7. Condition (C) -- CHAPTER 8. Cellular gradients are -- C0-generic -- CHAPTER 9. Properties of cellular gradients -- Part 4. Circle-valued Morse maps and Novikov -- complexes -- CHAPTER 10. Completions of rings, modules and -- complexes -- CHAPTER 11. The Novikov complex of a circle-valued -- Morse map -- CHAPTER 12. Cellular gradients of circle-valued -- Morse functions and the Rationality Theorem -- CHAPTER 13. Counting closed orbits of the gradient -- flow -- CHAPTER 14. Selected topics in the Morse-Novikov -- theory -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star In the early 1920s M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the early 1980s. Nowadays, it is a constantly growing field of contemporary mathematics with applications and connections to many geometrical problems such as Arnold's conjecture in the theory of Lagrangian intersections, fibrations of manifolds over the circle, dynamical zeta functions, and the theory of knots and links in the three-dimensional sphere. The aim of the book is to give a systematic treatment of geometric foundations of the subject and recent research results. The book is accessible to first year graduate students specializing in geometry and topology. 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) Manifolds (Mathematics). Morse theory. Differentialgeometrie. Morsetheorie. MATHEMATICS / Geometry / Differential. bisacsh Differential geometry. 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 2008 9783110212129 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 9783110212136 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 9783110209082 ZDB-23-DMN print 9783110158076 https://doi.org/10.1515/9783110197976 https://www.degruyter.com/isbn/9783110197976 Cover https://www.degruyter.com/document/cover/isbn/9783110197976/original |
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English |
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Pajitnov, Andrei V., Pajitnov, Andrei V., |
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Pajitnov, Andrei V., Pajitnov, Andrei V., Circle-valued Morse Theory / De Gruyter Studies in Mathematics , Frontmatter -- Contents -- Preface -- Introduction -- Part 1. Morse functions and vector fields on -- manifolds -- CHAPTER 1. Vector fields and C0 topology -- CHAPTER 2. Morse functions and their -- gradients -- CHAPTER 3. Gradient flows of real-valued Morse -- functions -- Part 2. Transversality, handles, Morse -- complexes -- CHAPTER 4. The Kupka-Smale transversality theory -- for gradient flows -- CHAPTER 5. Handles -- CHAPTER 6. The Morse complex of a Morse -- function -- Part 3. Cellular gradients -- CHAPTER 7. Condition (C) -- CHAPTER 8. Cellular gradients are -- C0-generic -- CHAPTER 9. Properties of cellular gradients -- Part 4. Circle-valued Morse maps and Novikov -- CHAPTER 10. Completions of rings, modules and -- CHAPTER 11. The Novikov complex of a circle-valued -- Morse map -- CHAPTER 12. Cellular gradients of circle-valued -- Morse functions and the Rationality Theorem -- CHAPTER 13. Counting closed orbits of the gradient -- flow -- CHAPTER 14. Selected topics in the Morse-Novikov -- theory -- Backmatter |
author_facet |
Pajitnov, Andrei V., Pajitnov, Andrei V., |
author_variant |
a v p av avp a v p av avp |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Pajitnov, Andrei V., |
title |
Circle-valued Morse Theory / |
title_full |
Circle-valued Morse Theory / Andrei V. Pajitnov. |
title_fullStr |
Circle-valued Morse Theory / Andrei V. Pajitnov. |
title_full_unstemmed |
Circle-valued Morse Theory / Andrei V. Pajitnov. |
title_auth |
Circle-valued Morse Theory / |
title_alt |
Frontmatter -- Contents -- Preface -- Introduction -- Part 1. Morse functions and vector fields on -- manifolds -- CHAPTER 1. Vector fields and C0 topology -- CHAPTER 2. Morse functions and their -- gradients -- CHAPTER 3. Gradient flows of real-valued Morse -- functions -- Part 2. Transversality, handles, Morse -- complexes -- CHAPTER 4. The Kupka-Smale transversality theory -- for gradient flows -- CHAPTER 5. Handles -- CHAPTER 6. The Morse complex of a Morse -- function -- Part 3. Cellular gradients -- CHAPTER 7. Condition (C) -- CHAPTER 8. Cellular gradients are -- C0-generic -- CHAPTER 9. Properties of cellular gradients -- Part 4. Circle-valued Morse maps and Novikov -- CHAPTER 10. Completions of rings, modules and -- CHAPTER 11. The Novikov complex of a circle-valued -- Morse map -- CHAPTER 12. Cellular gradients of circle-valued -- Morse functions and the Rationality Theorem -- CHAPTER 13. Counting closed orbits of the gradient -- flow -- CHAPTER 14. Selected topics in the Morse-Novikov -- theory -- Backmatter |
title_new |
Circle-valued Morse Theory / |
title_sort |
circle-valued morse theory / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2008 |
physical |
1 online resource (454 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- Introduction -- Part 1. Morse functions and vector fields on -- manifolds -- CHAPTER 1. Vector fields and C0 topology -- CHAPTER 2. Morse functions and their -- gradients -- CHAPTER 3. Gradient flows of real-valued Morse -- functions -- Part 2. Transversality, handles, Morse -- complexes -- CHAPTER 4. The Kupka-Smale transversality theory -- for gradient flows -- CHAPTER 5. Handles -- CHAPTER 6. The Morse complex of a Morse -- function -- Part 3. Cellular gradients -- CHAPTER 7. Condition (C) -- CHAPTER 8. Cellular gradients are -- C0-generic -- CHAPTER 9. Properties of cellular gradients -- Part 4. Circle-valued Morse maps and Novikov -- CHAPTER 10. Completions of rings, modules and -- CHAPTER 11. The Novikov complex of a circle-valued -- Morse map -- CHAPTER 12. Cellular gradients of circle-valued -- Morse functions and the Rationality Theorem -- CHAPTER 13. Counting closed orbits of the gradient -- flow -- CHAPTER 14. Selected topics in the Morse-Novikov -- theory -- Backmatter |
isbn |
9783110197976 9783110494938 9783110238570 9783110238471 9783110637205 9783110212129 9783110212136 9783110209082 9783110158076 |
issn |
0179-0986 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA331 |
callnumber-sort |
QA 3331 P35 42006EB |
url |
https://doi.org/10.1515/9783110197976 https://www.degruyter.com/isbn/9783110197976 https://www.degruyter.com/document/cover/isbn/9783110197976/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514/.74 |
dewey-sort |
3514 274 |
dewey-raw |
514/.74 |
dewey-search |
514/.74 |
doi_str_mv |
10.1515/9783110197976 |
oclc_num |
979969284 |
work_keys_str_mv |
AT pajitnovandreiv circlevaluedmorsetheory |
status_str |
n |
ids_txt_mv |
(DE-B1597)32310 (OCoLC)979969284 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
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 2008 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 |
is_hierarchy_title |
Circle-valued Morse Theory / |
container_title |
Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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