The Resource An invitation to Morse theory, Liviu I. Nicolaescu
An invitation to Morse theory, Liviu I. Nicolaescu
Resource Information
The item An invitation to Morse theory, Liviu I. Nicolaescu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item An invitation to Morse theory, Liviu I. Nicolaescu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 "This selfcontained 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. PicardLefschetz theory. This is the first textbook to include topics such as MorseSmale flows, minmax 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
 Language
 eng
 Extent
 xiv, 241 pages
 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
 MorseSmale dynamics
 MorseFloer homology
 MorseBott functions
 MinMax theory
 3. Applications
 The cohomology of complex grassmannians
 Lefschetz hyderplane theorem
 Symplectic manifolds and Hamiltonian flows
 Morse theory of moment maps
 S1Equivariant 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 PicardLefschetz formulæ
 5. Exercises and solutions
 Exercises
 Solutions to selected exercises
 Isbn
 9780387495101
 Label
 An invitation to Morse theory
 Title
 An invitation to Morse theory
 Statement of responsibility
 Liviu I. Nicolaescu
 Language
 eng
 Summary
 "This selfcontained 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. PicardLefschetz theory. This is the first textbook to include topics such as MorseSmale flows, minmax 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
 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
 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  MorseSmale dynamics  MorseFloer homology  MorseBott functions  MinMax theory  3. Applications  The cohomology of complex grassmannians  Lefschetz hyderplane theorem  Symplectic manifolds and Hamiltonian flows  Morse theory of moment maps  S1Equivariant 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 PicardLefschetz 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
 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  MorseSmale dynamics  MorseFloer homology  MorseBott functions  MinMax theory  3. Applications  The cohomology of complex grassmannians  Lefschetz hyderplane theorem  Symplectic manifolds and Hamiltonian flows  Morse theory of moment maps  S1Equivariant 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 PicardLefschetz 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
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/AninvitationtoMorsetheoryLiviuI./EdS0pztueKc/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/AninvitationtoMorsetheoryLiviuI./EdS0pztueKc/">An invitation to Morse theory, Liviu I. Nicolaescu</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>