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About this product
- Author(s)A. N. Varchenko,S. M. Gusein-Zade,V. I. Arnold
- PublisherSpringer-Verlag New York Inc.
- Date of Publication01/08/2012
- Series TitleMonographs in Mathematics
- Series Part/Volume Number83
- Place of PublicationNew York
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Note5 black & white illustrations, biography
- Weight860 g
- Width170 mm
- Height244 mm
- Spine25 mm
- Format DetailsTrade paperback (US)
- Edition StatementSoftcover reprint of the original 1st ed. 1988
- Table Of ContentsI The topological structure of isolated critical points of functions.- 1 Elements of the theory of Picard-Lefschetz.- 2 The topology of the non-singular level set and the variation operator of a singularity.- 3 The bifurcation sets and the monodromy group of a singularity.- 4 The intersection matrices of singularities of functions of two variables.- 5 The intersection forms of boundary singularities and the topology of complete intersections.- II Oscillatory integrals.- 6 Discussion of results.- 7 Elementary integrals and the resolution of singularities of the phase.- 8 Asymptotics and Newton polyhedra.- 9 The singular index, examples.- III Integrals of holomorphic forms over vanishing cycles.- 10 The simplest properties of the integrals.- 11 Complex oscillatory integrals.- 12 Integrals and differential equations.- 13 The coefficients of series expansions of integrals, the weighted and Hodge filtrations and the spectrum of a critical point.- 14 The mixed Hodge structure of an isolated critical point of a holomorphic function.- 15 The period map and the intersection form.- References.
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