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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.
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.
 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, pseudoholomorphic curves, and GromovWitten 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, nonFredholm behavior, true and false critical points at infinity, and topological implications. An increasing convergence with regular and singular Yamabetype problems is discussed, and the intersection between contact form and Riemannian geometry is emphasized, with a specific focus on a unified approach to noncompactness 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
 Language

 eng
 eng
 Edition
 1st ed. 2003.
 Extent
 1 online resource (IX, 225 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 Introduction, Statement of Results, and Discussion of Related Hypotheses
 1 Topological results
 2 Intermediate hypotheses (A4), (A4)’ (A5), (A6)
 3 The nonFredholm 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
 Isbn
 9781461200215
 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
 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, pseudoholomorphic curves, and GromovWitten 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, nonFredholm behavior, true and false critical points at infinity, and topological implications. An increasing convergence with regular and singular Yamabetype problems is discussed, and the intersection between contact form and Riemannian geometry is emphasized, with a specific focus on a unified approach to noncompactness 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
 http://library.link/vocab/creatorName
 Bahri, Abbas
 Dewey number
 516.36
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 CQ5beCWQ6K0
 Image bit depth
 0
 Language note
 English
 LC call number
 QA641670
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Progress in Nonlinear Differential Equations and Their Applications,
 Series volume
 53
 http://library.link/vocab/subjectName

 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)
 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 nonFredholm 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
 10.1007/9781461200215
 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
 (DEHe213)9781461200215
 (MiAaPQ)EBC3074662
 (EXLCZ)993400000000088949
 Label
 Flow Lines and Algebraic Invariants in Contact Form Geometry, by Abbas Bahri, (electronic resource)
 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 nonFredholm 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
 10.1007/9781461200215
 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
 (DEHe213)9781461200215
 (MiAaPQ)EBC3074662
 (EXLCZ)993400000000088949
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/FlowLinesandAlgebraicInvariantsinContact/E_AB4x_UuQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/FlowLinesandAlgebraicInvariantsinContact/E_AB4x_UuQ/">Flow Lines and Algebraic Invariants in Contact Form Geometry, by Abbas Bahri, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>