The Resource Holomorphic Curves in Low Dimensions : From Symplectic Ruled Surfaces to Planar Contact Manifolds, by Chris Wendl, (electronic resource)

Holomorphic Curves in Low Dimensions : From Symplectic Ruled Surfaces to Planar Contact Manifolds, by Chris Wendl, (electronic resource)

Label
Holomorphic Curves in Low Dimensions : From Symplectic Ruled Surfaces to Planar Contact Manifolds
Title
Holomorphic Curves in Low Dimensions
Title remainder
From Symplectic Ruled Surfaces to Planar Contact Manifolds
Statement of responsibility
by Chris Wendl
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Member of
http://library.link/vocab/creatorName
Wendl, Chris
Image bit depth
0
LC call number
QA641-670
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Lecture Notes in Mathematics,
Series volume
2216
http://library.link/vocab/subjectName
  • Mathematics
  • Global analysis (Mathematics)
  • Manifolds (Mathematics)
  • Geometry, Differential
  • Complex manifolds
  • Mathematics
  • Differential Geometry
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Global Analysis and Analysis on Manifolds
Label
Holomorphic Curves in Low Dimensions : From Symplectic Ruled Surfaces to Planar Contact Manifolds, by Chris Wendl, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Introduction -- 2 Background on Closed Pseudoholomorphic Curves -- 3 Blowups and Lefschetz Fibrations -- 4 Compactness -- 5 Exceptional Spheres -- 6 Rational and Ruled Surfaces -- 7 Uniruled Symplectic 4-Manifolds -- 8 Holomorphic Curves in Symplectic Cobordisms -- 9 Contact 3-Manifolds and Symplectic Fillings -- Appendix -- Bibliography -- Index
Dimensions
unknown
Extent
XIII, 294 p. 33 illus., 31 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319913711
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-91371-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-91371-1
Label
Holomorphic Curves in Low Dimensions : From Symplectic Ruled Surfaces to Planar Contact Manifolds, by Chris Wendl, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Introduction -- 2 Background on Closed Pseudoholomorphic Curves -- 3 Blowups and Lefschetz Fibrations -- 4 Compactness -- 5 Exceptional Spheres -- 6 Rational and Ruled Surfaces -- 7 Uniruled Symplectic 4-Manifolds -- 8 Holomorphic Curves in Symplectic Cobordisms -- 9 Contact 3-Manifolds and Symplectic Fillings -- Appendix -- Bibliography -- Index
Dimensions
unknown
Extent
XIII, 294 p. 33 illus., 31 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319913711
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-91371-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-91371-1

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