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Lagrange Legendre Characterist

Lagrange Legendre Characterist


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About the Book

This book contains Vassilyev's new definition of higher-dimensional classes analogous to the Maslov class using catastrophe theory. Opening with an introduction to symplectic and contact geometry, it goes on to describe the method used - the construction of a cochain complex generated by elements of the Thom-Arnol'd list of catastrophes, and shows how the designed characteristic classes correspond to the cohomology of this complex. This book should interest specialists in mathematical catastrophe theory, algebraic and differential topology, and geometrical and wave optics.

Table of Contents:
Part 1 Lagrange and Legendre manifolds, singularities and cobordisms: symplectic manifolds and Lagrange manifolds; singularities of smooth functions; Legendre manifolds; Maslov index; Lagrange and Legendre cobordisms; Arnol'd's construction of the Maslov index, Borel-Fuchs classes, and Legendre cobordism groups in J1 (Rn,R). Part 2 Lagrange and Legendre characteristic classes dual to the singularities of caustics and wave fronts: stratifications, semi-analytic sets and semi-algebraic sets; universal complexes of co-orientable classes; generators of the complexes; calculation of the cohomology of universal complexes; the complexes N(Go),v(G0) of non-cooriented classes; the complexes w, v and characteristic classes. Part 3 Self-intersection of wave fronts and Legendre (Lagrange) - characteristic numbers: complexes of multisingularities of wave fronts; cohomology of the complexes; reduction of the Lagrange problem to the Legendre problem; cycles of multisingularities and multiplication in the homology of the base of the Legendre bundle; summary of results on the realizability of characteristic numbers and classes. Part 4 Derived characteristic classes and Borel-Fuchs classes: multiplication in universal complexes; Steifel-Whitney and Pontryagin classes of normal bundles to singularity classes; characteristic classes of normal bundles and classifying spaces connected with singularity classes; Steenrod squares of characteristic classes; cohomology of Lagrange Grassmannians; Thom polynomials.


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Product Details
  • ISBN-13: 9782881246616
  • Publisher: Gordon and Breach
  • Publisher Imprint: Gordon & Breach Science Publishers Ltd
  • Language: English
  • Weight: 454 gr
  • ISBN-10: 2881246613
  • Publisher Date: 01 Feb 1988
  • Binding: Hardback
  • Returnable: N


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