Singularities of Differentiable Maps, Volume 2

Monodromy and Asymptotics of Integrals

Authors:

ISBN: 978-0-8176-8342-9 (Print) 978-0-8176-8343-6 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-x

  2. The Topological Structure of Isolated Critical Points of Functions

    1. Front Matter

      Pages 1-8

    2. No Access

      Book Chapter

      Pages 9-28

      Elements of the theory of Picard-Lefschetz

    3. No Access

      Book Chapter

      Pages 29-66

      The topology of the non-singular level set and the variation operator of a singularity

    4. No Access

      Book Chapter

      Pages 67-113

      The bifurcation sets and the monodromy group of a singularity

    5. No Access

      Book Chapter

      Pages 114-138

      The intersection matrices of singularities of functions of two variables

    6. No Access

      Book Chapter

      Pages 139-167

      The intersection forms of boundary singularities and the topology of complete intersections

  3. Oscillatory Integrals

    1. Front Matter

      Pages 169-169

    2. No Access

      Book Chapter

      Pages 170-214

      Discussion of results

    3. No Access

      Book Chapter

      Pages 215-232

      Elementary integrals and the resolution of singularities of the phase

    4. No Access

      Book Chapter

      Pages 233-262

      Asymptotics and Newton polyhedra

    5. No Access

      Book Chapter

      Pages 263-267

      The singular index, examples

  4. Integrals of Holomorphic forms over Vanishing cycles

    1. Front Matter

      Pages 269-269

    2. No Access

      Book Chapter

      Pages 270-295

      The simplest properties of the integrals

    3. No Access

      Book Chapter

      Pages 296-315

      Complex oscillatory integrals

    4. No Access

      Book Chapter

      Pages 316-350

      Integrals and differential equations

    5. No Access

      Book Chapter

      Pages 351-393

      The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectrum of a critical point

    6. No Access

      Book Chapter

      Pages 394-440

      The mixed Hodge structure of an isolated critical point of a holomorphic function

    7. No Access

      Book Chapter

      Pages 441-463

      The period map and the intersection form

  5. Back Matter

    Pages 465-492