Singularities and foliations : geometry, topology and applications : BMMS 2/NBMS 3, Salvador, Brazil, 2015 /: geometry, topology and applications : BMMS 2/NBMS 3, Salvador, Brazil, 2015. ([2018])

• Record Type: Book
• Further Information: Note: Raimundo Nonato Araújo dos Santos, Aurélio Menegon Neto, David Mond, Marcelo J. Saia, Jawad Snoussi, editors.
• Editors: Santos, Raimundo Nonato Araújo dos; Neto, Aurélio Menegon; Mond, D (David); Saia, Marcelo José; Snoussi, Jawad
• Other Names: Brazil-Mexico Meeting on Singularities, 2nd; Singularity Theory Meeting, 3rd
• Contents: Intro; Preface; Acknowledgements; Contents; Lecture Notes: Geometry, Topology, and Algebraic Aspects of Singularities; Combinatorial Models in the Topological Classification of Singularities of Mappings; 1 Introduction; 2 Stability; 3 Finite Determinacy; 4 The Cone Structure Theorem for Map Germs with Isolated Zeros; 5 Gauss Words; 6 Reeb Graphs; 7 The Cone Structure Theorem for Map Germs with Non Isolated Zeros; References; Topology of Real Singularities; 1 Introduction; 2 The Brouwer Degree, the Poincaré-Hopf Index and Morse Functions; 2.1 The Brouwer Degree; 2.2 The Poincaré-Hopf Index. 2.3 Morse Functions3 The Eisenbud-Levine Formula, the Khimshiashvili Formula and Some Generalizations; 3.1 The Eisenbud-Levine Formula; 3.2 The Khimshiashvili Formula; 3.3 Non-isolated Critical Points; 3.4 Semi-analytic Versions; 4 Degree Formulas and Signature Formulas for the Euler Characteristic of Algebraic Sets and Semi-algebraic Sets; 4.1 Case of 0-Dimensional Algebraic Sets; 4.2 Case of a Compact Algebraic Set; 4.3 Case of a Smooth Complete Intersection; 4.4 Case of Complete Intersections with Isolated Singularities; 4.5 Semi-algebraic Versions; 5 Topology of the Real Milnor Fibration. 5.1 Milnor's Conditions (a) and (b) and the Fibration Theorem5.2 Topology of the Real Milnor Fibre; References; Equisingularity and the Theory of Integral Closure; 1 Equisingularity Conditions; 2 The Theory of Integral Closure of Ideals and Modules; 3 Multiplicities, Integral Closure and the Multiplicity-Polar Theorem; 4 Afterword: Examples of the Point of View of the Introduction; References; Surveys Papers on Advances in Foliations and Singularity Theory: Topology Geometry and Applications; A Brief Survey on Singularities of Geodesic Flows in Smooth Signature Changing Metrics on 2-Surfaces. 1 Introduction2 Definition of Geodesics; 3 Equation of Isotropic Lines; 4 Singular Points of the Geodesic Flow; 4.1 The Case C; 4.2 The Case D; 4.3 Example: Clairaut Type; References; Orbital Formal Rigidity for Germs of Holomorphic and Real Analytic Vector Fields; 1 Introduction; 2 Analytic Equivalence and Formal Rigidity; 2.1 Holomorphic Vector Fields; 2.2 Real Analytic Vector Fields; 2.3 Formal Rigidity and Real-Formal Rigidity; 3 Formal Rigidity for Elementary Singularities; 3.1 Poincaré-Dulac's and Brjuno's Theorems; 3.2 Cases Where Formal Rigidity Fails.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 516.3/5; Mathematics; Singularities (Mathematics) -- Congresses; Foliations (Mathematics) -- Congresses; Topology -- Congresses; MATHEMATICS -- Geometry -- General; Foliations (Mathematics); Singularities (Mathematics); Topology; Mathematics -- Geometry -- Algebraic; Mathematics -- Topology; Algebraic geometry; Analytic geometry; Algebraic topology; Geometry, algebraic; Cell aggregation_xMathematics; Algebraic topology; Electronic books; Conference papers and proceedings
• Languages: English
• ISBNs: 9783319736396; 3319736396
• Related ISBNs: 9783319736389; 3319736388
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed March, 27, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.