The Resource Flow Lines and Algebraic Invariants in Contact Form Geometry, by Abbas Bahri, (electronic resource)

# Flow Lines and Algebraic Invariants in Contact Form Geometry, by Abbas Bahri, (electronic resource) Resource Information The item Flow Lines and Algebraic Invariants in Contact Form Geometry, by Abbas Bahri, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.

Label
Flow Lines and Algebraic Invariants in Contact Form Geometry
Title
Flow Lines and Algebraic Invariants in Contact Form Geometry
Statement of responsibility
by Abbas Bahri
Creator
Author
Author
Subject
Language
• eng
• eng
Summary
This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, this work develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields. The book opens with a review of prior results and then proceeds through an examination of variational problems, non-Fredholm behavior, true and false critical points at infinity, and topological implications. An increasing convergence with regular and singular Yamabe-type problems is discussed, and the intersection between contact form and Riemannian geometry is emphasized, with a specific focus on a unified approach to non-compactness in both disciplines. Fully detailed, explicit proofs and a number of suggestions for further research are provided throughout. Rich in open problems and written with a global view of several branches of mathematics, this text lays the foundation for new avenues of study in contact form geometry. Graduate students and researchers in geometry, partial differential equations, and related fields will benefit from the book's breadth and unique perspective
Member of
Bahri, Abbas
Dewey number
516.36
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
CQ5beCWQ6K0
Image bit depth
0
Language note
English
LC call number
QA641-670
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Progress in Nonlinear Differential Equations and Their Applications,
Series volume
53
• Global differential geometry
• Differential Equations
• Differential equations, partial
• Algebraic topology
• Differential Geometry
• Ordinary Differential Equations
• Partial Differential Equations
• Algebraic Topology
Label
Flow Lines and Algebraic Invariants in Contact Form Geometry, by Abbas Bahri, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
Introduction, Statement of Results, and Discussion of Related Hypotheses -- 1 Topological results -- 2 Intermediate hypotheses (A4), (A4)’ (A5), (A6) -- 3 The non-Fredholm character of this variational problem, the associated cones, condition (A5) (discussion and removal) -- 4.a Hypothesis $$\overline {(A4)}$$ and statement of the most general results, discussion of $$\overline {(A4)}$$ -- 4.b Discussion of (A2), (A3), and $$\overline {(A4)}$$ -- Outline of the Book -- I Review of the Previous Results, Some Open Questions -- I.A Setup of the Variational Problem -- I.B The Flow Z0 of [2]: Critical Points at Infinity, False and True -- II Intermediate Section: Recalling the Results Described in the Introduction, Outlining the Content of the Next Sections and How These Results are Derived -- III Technical Study of the Critical Points at Infinity: Variational Theory without the Fredholm Hypothesis -- III.A True Critical Points at Infinity -- III.B False Critical Points at Infinity of the Second Kind -- IV Removal of (A5) -- IV.1 The Difference of Topology Due to a False Critical Point at Infinity of the Third Kind -- IV.2 Completion of the Removal of (A5) -- IV.3 Critical Points at Infinity of Mixed Type -- IV.4 (A5) and the Critical Points at Infinity of the Third Kind or of Mixed Type -- V Conditions (A2)—(A3)—(A4)—(A6) -- V.1 An Outline for the Removal of (A2) -- V.2 Discussion of (A3) -- V.3 Weakening Condition (A4) -- V.4 Removing Condition (A6) -- References
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (IX, 225 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461200215
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0021-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
• (CKB)3400000000088949
• (SSID)ssj0001296717
• (PQKBManifestationID)11716451
• (PQKBTitleCode)TC0001296717
• (PQKBWorkID)11353637
• (PQKB)11126093
• (DE-He213)978-1-4612-0021-5
• (MiAaPQ)EBC3074662
• (EXLCZ)993400000000088949
Label
Flow Lines and Algebraic Invariants in Contact Form Geometry, by Abbas Bahri, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
Introduction, Statement of Results, and Discussion of Related Hypotheses -- 1 Topological results -- 2 Intermediate hypotheses (A4), (A4)’ (A5), (A6) -- 3 The non-Fredholm character of this variational problem, the associated cones, condition (A5) (discussion and removal) -- 4.a Hypothesis $$\overline {(A4)}$$ and statement of the most general results, discussion of $$\overline {(A4)}$$ -- 4.b Discussion of (A2), (A3), and $$\overline {(A4)}$$ -- Outline of the Book -- I Review of the Previous Results, Some Open Questions -- I.A Setup of the Variational Problem -- I.B The Flow Z0 of [2]: Critical Points at Infinity, False and True -- II Intermediate Section: Recalling the Results Described in the Introduction, Outlining the Content of the Next Sections and How These Results are Derived -- III Technical Study of the Critical Points at Infinity: Variational Theory without the Fredholm Hypothesis -- III.A True Critical Points at Infinity -- III.B False Critical Points at Infinity of the Second Kind -- IV Removal of (A5) -- IV.1 The Difference of Topology Due to a False Critical Point at Infinity of the Third Kind -- IV.2 Completion of the Removal of (A5) -- IV.3 Critical Points at Infinity of Mixed Type -- IV.4 (A5) and the Critical Points at Infinity of the Third Kind or of Mixed Type -- V Conditions (A2)—(A3)—(A4)—(A6) -- V.1 An Outline for the Removal of (A2) -- V.2 Discussion of (A3) -- V.3 Weakening Condition (A4) -- V.4 Removing Condition (A6) -- References
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (IX, 225 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461200215
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0021-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
• (CKB)3400000000088949
• (SSID)ssj0001296717
• (PQKBManifestationID)11716451
• (PQKBTitleCode)TC0001296717
• (PQKBWorkID)11353637
• (PQKB)11126093
• (DE-He213)978-1-4612-0021-5
• (MiAaPQ)EBC3074662
• (EXLCZ)993400000000088949

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