Singularities of Differentiable Maps, Volume 2: Monodromy and Asymptotics of Integrals
Springer Science & Business Media, May 16, 2012 - Mathematics - 492 pages
The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originally published as Volume 82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how they function.
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Part II Oscillatory integrals
Part III Integrals of holomorphic forms over vanishing cycles
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amplitude analytic asymptotic series Bernstein polynomial boundary classical monodromy operator coefficients cohomological Milnor fibration cohomology complex cone coordinates Corollary corresponding covariantly constant sections critical point critical values curve D-diagram defined definition diffeomorphic dimension distinguished basis eigenvalue equations equivalent example fibre finite follows formula function f Gauss-Manin connection geometric sections germ f Hodge filtration holomorphic differential n-form holomorphic function homology class homology group homotopy hyperplane hypersurface intersection form intersection number isomorphism Lemma Let f Let us consider Let us denote Let us suppose level hypersurface linear manifold F mixed Hodge structure monodromy group monomial multiplicity Newton polyhedron non-critical value non-singular level manifold number of variables origin oscillation index oscillatory integral pair parameter period map perturbation phase Picard-Fuchs Picard-Fuchs equations polynomial preimage proved quasihomogeneous resolution simple singularities singular point singularity f subfibration subspace sufficiently small Taylor series trivialisation vanishing cycles versal deformation weight filtration zero level