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The Resource An invitation to Morse theory, Liviu I. Nicolaescu

An invitation to Morse theory, Liviu I. Nicolaescu

Label
An invitation to Morse theory
Title
An invitation to Morse theory
Statement of responsibility
Liviu I. Nicolaescu
Creator
Subject
Language
eng
Summary
"This self-contained treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory (over the reals). The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. This is the first textbook to include topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds"--Publisher description
Member of
Cataloging source
UKM
http://library.link/vocab/creatorName
Nicolaescu, Liviu I
Dewey number
514.74
Index
index present
LC call number
QA331
LC item number
.N498 2007
Literary form
non fiction
Nature of contents
bibliography
Series statement
Universitext
http://library.link/vocab/subjectName
  • Morse theory
  • Morse, Théorie de
  • Morse theorie
Label
An invitation to Morse theory, Liviu I. Nicolaescu
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages [233]-235) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Notations and conventions -- 1. Morse functions -- The local structure of Morse functions -- Existence of Morse functions -- 2. The topology of Morse functions -- Surgery, handle attachment, and cobordisms -- The topology of sublevel sets -- Morse inequalities -- Morse-Smale dynamics -- Morse-Floer homology -- Morse-Bott functions -- Min-Max theory -- 3. Applications -- The cohomology of complex grassmannians -- Lefschetz hyderplane theorem -- Symplectic manifolds and Hamiltonian flows -- Morse theory of moment maps -- S1-Equivariant localization -- 4. Basics of complex Morse theory -- Some fundamental constructions -- Topological applications of Lefschetz pencils -- The hard Lefschetz theorem -- Vanishing cycles and local monodromy -- Proof of the Picard-Lefschetz formulæ -- 5. Exercises and solutions -- Exercises -- Solutions to selected exercises
Control code
76851150
Dimensions
24 cm
Extent
xiv, 241 pages
Isbn
9780387495101
Isbn Type
(ebk.)
Lccn
2006938271
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
System control number
(OCoLC)76851150
Label
An invitation to Morse theory, Liviu I. Nicolaescu
Publication
Bibliography note
Includes bibliographical references (pages [233]-235) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Notations and conventions -- 1. Morse functions -- The local structure of Morse functions -- Existence of Morse functions -- 2. The topology of Morse functions -- Surgery, handle attachment, and cobordisms -- The topology of sublevel sets -- Morse inequalities -- Morse-Smale dynamics -- Morse-Floer homology -- Morse-Bott functions -- Min-Max theory -- 3. Applications -- The cohomology of complex grassmannians -- Lefschetz hyderplane theorem -- Symplectic manifolds and Hamiltonian flows -- Morse theory of moment maps -- S1-Equivariant localization -- 4. Basics of complex Morse theory -- Some fundamental constructions -- Topological applications of Lefschetz pencils -- The hard Lefschetz theorem -- Vanishing cycles and local monodromy -- Proof of the Picard-Lefschetz formulæ -- 5. Exercises and solutions -- Exercises -- Solutions to selected exercises
Control code
76851150
Dimensions
24 cm
Extent
xiv, 241 pages
Isbn
9780387495101
Isbn Type
(ebk.)
Lccn
2006938271
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
System control number
(OCoLC)76851150

Library Locations

    • Mathematical Sciences LibraryBorrow it
      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
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