简介
Presented at a seminar held at the Steklov Mathematical Institute, Moscow, the 14 papers here reflect Novikov's own wide range of interests in geometry, topology and mathematical physics. Topics include a study of Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups, equivariant complex structures on homogeneous spaces and their cobordism classes, the universality of critical behavior in Hamiltonian partial differential equations, the geometry of V-systems, spectral conservation laws for periodic nonlinear equations of the Melknikov type, an equivariant version of the monodromy zeta function, certain simplectic algebras and string topology operations, differential forms and odd symplectic geometry, Abelian solutions of the KP equation, deformations of the Whitham systems in the almost-linear case, Frobenius manifolds in pseudo-Euclidian spaces, the Gibbons-Tsarev system, two-dimensional Toda chains, and certain current algebras related to finite-zone integration. Suitable for graduate students and researchers. Annotation 漏2008 Book News, Inc., Portland, OR (booknews.com)
目录
Table Of Contents:
Preface vii
Hurwitz Numbers for Regular Coverings of Surfaces by Seamed Surfaces and Cardy-Frobenius Algebras of Finite Groups 1(26)
A. V. Alexeevski
S. M. Natanzon
Equivariant Complex Structures on Homogeneous Spaces and Their Cobordism Classes 27(32)
Victor M. Buchstaber
Svjetlana Terzic
On Universality of Critical Behaviour in Hamiltonian PDEs 59(52)
Boris Dubrovin
On the geometry of V-systems 111(14)
M. Feigin
A. P. Veselov
Spectral Conservation Laws for Periodic Nonlinear Equations of the Melnikov Type 125(14)
P. G. Grinevich
I. A. Taimanov
An Equivariant Version of the Monodromy Zeta Function 139(8)
S. M. Gusein-Zade
I. Luengo
A. Melle-Hernandez
Symplectic A∞-Algebras and String Topology Operations 147(12)
Alastair Hamilton
Andrey Lazarev
Differential Forms and Odd Symplectic Geometry 159(1)
Hovhannes M. Khudaverdian
Theodore Th. Voronov
Abelian Solutions of Odd Symplectic Geometry 159(14)
Hovhannes M. Khudaverdian
Theodore Th. Voronov
Abelian Solutions of the KP Equation 173(20)
I. Krichever
T. Shiota
Deformations of the Whitham Systems in the Almost Linear Case 193(20)
A. Ya. Maltsev
Frobenius Manifolds as a Special Class of Submanifolds in Pseudo-Euclidean Spaces 213(34)
O. I. Mokhov
Integrability of the Gibbons-Tsarev System 247(14)
Maxim V. Pavlov
Toda Chain and Associated Commutator Identity 261(10)
A. K. Pogrebkov
On Certain Current Algebras Related to Finite-Zone Integration 271
Oleg K. Sheinman
Preface vii
Hurwitz Numbers for Regular Coverings of Surfaces by Seamed Surfaces and Cardy-Frobenius Algebras of Finite Groups 1(26)
A. V. Alexeevski
S. M. Natanzon
Equivariant Complex Structures on Homogeneous Spaces and Their Cobordism Classes 27(32)
Victor M. Buchstaber
Svjetlana Terzic
On Universality of Critical Behaviour in Hamiltonian PDEs 59(52)
Boris Dubrovin
On the geometry of V-systems 111(14)
M. Feigin
A. P. Veselov
Spectral Conservation Laws for Periodic Nonlinear Equations of the Melnikov Type 125(14)
P. G. Grinevich
I. A. Taimanov
An Equivariant Version of the Monodromy Zeta Function 139(8)
S. M. Gusein-Zade
I. Luengo
A. Melle-Hernandez
Symplectic A∞-Algebras and String Topology Operations 147(12)
Alastair Hamilton
Andrey Lazarev
Differential Forms and Odd Symplectic Geometry 159(1)
Hovhannes M. Khudaverdian
Theodore Th. Voronov
Abelian Solutions of Odd Symplectic Geometry 159(14)
Hovhannes M. Khudaverdian
Theodore Th. Voronov
Abelian Solutions of the KP Equation 173(20)
I. Krichever
T. Shiota
Deformations of the Whitham Systems in the Almost Linear Case 193(20)
A. Ya. Maltsev
Frobenius Manifolds as a Special Class of Submanifolds in Pseudo-Euclidean Spaces 213(34)
O. I. Mokhov
Integrability of the Gibbons-Tsarev System 247(14)
Maxim V. Pavlov
Toda Chain and Associated Commutator Identity 261(10)
A. K. Pogrebkov
On Certain Current Algebras Related to Finite-Zone Integration 271
Oleg K. Sheinman
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