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Manin Yu.I. — Frobenius manifolds, quantum cohomology, and moduli spaces
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Название: Frobenius manifolds, quantum cohomology, and moduli spaces
Автор: Manin Yu.I.
Аннотация: Book News, Inc.
This monograph summarizes some of the developments that have taken place in quantum cohomology in the last decade, but does not explain the history or physical motivations. Manin begins by developing the local and global geometric and analytic theory of Frobenius manifolds, then introduces the more algebraic aspects< — >formal Frobenius manifolds, moduli spaces and their homology operads. The last two chapters focus on the algebraic geometric constructions of the Gromov-Witten invariants. — Copyright © 1999 Book News, Inc., Portland, OR All rights reserved
Product Description:
This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade.
The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the construction of quantum cohomology and reviews the algebraic geometry mechanisms involved in this construction (intersection and deformation theory of Deligne-Artin and Mumford stacks).
Yuri Manin is currently the director of the Max-Planck-Institut für Mathematik in Bonn, Germany. He has authored and coauthored 10 monographs and almost 200 research articles in algebraic geometry, number theory, mathematical physics, history of culture, and psycholinguistics. Manin's books, such as Cubic Forms: Algebra, Geometry, and Arithmetic (1974), A Course in Mathematical Logic (1977), Gauge Field Theory and Complex Geometry (1988), Elementary Particles: Mathematics, Physics and Philosophy (1989, with I. Yu. Kobzarev), Topics in Non-commutative Geometry (1991), and Methods of Homological Algebra (1996, with S. I. Gelfand), secured for him solid recognition as an excellent expositor. Undoubtedly the present book will serve mathematicians for many years to come.
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Рубрика: Математика /Алгебра /Алгебраическая геометрия /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 1999
Количество страниц: 303
Добавлена в каталог: 15.03.2005
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Предметный указатель
-covariance axiom for GW-invariants III.5.2 VI.1.2
299
A-model 0.1
Absolute stabilization V.1.7 V.4.6
Abstract correlation functions III.1.3
Admissible metric 1.5.4
Affine flat structure on supermanifold 1.1.2
Algebraic space V.5.5.3
Algebraic stack V.5.5
Artin stacks V.5.5
Associative pre-Frobenius manifold 1.1.3
Associativity (WDW) equations 0.2 1.1.3.1
Atlas V.5.5
B-model 0.1
Boundary morphism of moduli stacks V.4.7
Cartesian square of groupoids V.4.3.1 '
Central operations V.8.7
Chern classes V.8.6
Class of prestable map V.l.4.1
Classical linear operad IV.1.1.1
Classifying groupoid V.3.2.5
Co-identity 1.2.1.4
Cohomological correlators VI.2.2
Cohomological Field Theory (CohFT) 0.3.1 III.4.1
Combinatorial type of prestable curve III.2.5
Combinatorial type of prestable map V.1.5
Complete Cohomological Field Theory III.4.5
Configuration space IV.4.3
Correlation functions of CohFT III.4.1
Cycles on DM-stacks V.7.1.1
Cycles on schemes V.6.1
Cyclic -algebra III.1.2
Cyclic operad IV.2.6
d-spectrum of a Frobenius manifold III.4.10.4
Darboux — Egoroff’s equations 1.3.4
Degeneration Axiom for GW-invariants III.5.2 VI.
Deligne — Mumford (DM) stacks V.5.5
Differential Gerstenhaber — Batalin — Vilkovyski (dGBV) algebra III.9.5
Dilaton equation V.5.3
Dimension axiom for GW-invariants III.5.3
Direct sum diagram (of Saito’s frameworks) III.8.5
Direct sum of singularities III.8.6
Divisor axiom for GW-invariants III.5.3
Dual modular graph of prestable curve III.2.5
Dualizing sheaf V.l.l
Edge (of graph) III.2.1
Effectivity axiom for GW-invariants III.5.2 VI.1.2
Equivalence groupoid V.5.5.2
Euler field 1.2.2.1
Euler field in quantum cohomology 1.4.4 III.5.3.4
Evaluation morphism V.4.2.2
Excess intersection formula V.8.8
Extended structure connection 1.2.5.1
F-algebra 1.5.5
F-manifold 1.5.1
Flag (of graph) III.2.1
Flat families V.2.1 V.2.2
Flat functions and forms 1.1.3.1
Flat pullback V.6.1.5 V.7.1.5
Formal Frobenius manifold 0.4.1 III.
Formal Frobenius manifold of qc-type IH.5.4.1
Formal Laplace transform II.1.3
Frobenius manifold 0.4.1 1.1.3
Generalized correlators VI.6.1
Gepner’s Frobenius manifolds, III.8.4.1
Gerstenhaber — Batalin — Vilkovyski (GBV) algebra III.9.4
Gluing along pairs of sections V.2.3
Good monomials III.3.5.1
Graph III.2.1
Gravitational descendants VI.2.1
Gravity algebra III.1.9
Gromov — Witten (GW) correspondences III.5 VI.1.3
Gromov — Witten (GW) invariants III.5
Groupoid V.3.2
Groupoid of prestable curves V.3.2.1
Groupoid of prestable maps V.3.2.2
Groupoid of universal curves V.3.2.3
Gysin maps V.6.2 V.7.2
Gysin pushforward for operational Chow groups V.8.9.2
Hamiltonian structure of Schlesinger’s equations II.2.4 Homological Chow groups of schemes
Homological Chow groups of DM-stacks, V.7.1.3 Homological Chow groups of Artin stacks, V.7.3
Identity Axiom for GW-invariants, III.5.3 Identity on pre-FVobenius manifold, 1.2.1 Induced Frobenius structure, 1.1.7
Landin transform, II.5.5.6
Large phase space, VI.2.4
Legendre-type transformation, 1.5.4.2
Local regular imbedding (l.r.i.) of stacks, V.7.2
Logarithmic CohFT of rank one, III.6.1.4
Mapping to a Point Axiom for GW-invariants, III.5.3, VI.1.2
Markl’s operad, IV.2.5
Maurer-Cartan equations, III.9.1
Metric potential, 1.3.3
Modified dualizing sheaf, V.1.2
Modular graph, III.2.4
Moduli space Mo,n, 0.3
Morphism of groupoids, V.4.2, V.4.3
Morphism of operads, IV. 1.4
Motivic correlators, VI.2.2
Mumford classes, III.6.2
Normal bundle, V.6.2.1
Normal cone, V.6.2.1
Normalized CohFT of rank one, III.6.1.5
Novikov ring, III.5.2.1
Operational Chow groups, V.8.1 Orientation classes, V.8.1.1, V.8.1.2
Painleve VI equation, II.5.4
Partition function, IV.3.2.2
Perturbation series, V.3
Potential of qc-type, III.5.4.1
Potential pre-FVobenius manifold, 1.1.3
Potential, 0.2
Pre-FVobenius manifold, 1.1.3
Prestable curve, III.2.1
Prestable map, V.l.3.1
Primary fields, VI.2.1
Projection formulas, V.8.5, V.8.9.4
Proper pushforward for operational Chow groups, V.8.9.1
Proper pushforward, V.6.1.4, V.7.1.4, V.8.3
Pullback for operational Chow groups, V.8.4
Puncture equation, VI.5.1
Pushforward of operational Chow groups, V.8.9
Quantum cohomology 0.1 III.5
Quantum cohomology of projective spaces II.4
Rank one CohFT III.6.1
Rational equivalence of cycles on DM-stacks V.7.1.2
Rational equivalence of cycles on schemes V.6.1.2
Representable morphism of groupoids V.5.3
Rotation coefficients 1.3.4
Saito’s framework III.8.2.1
Schlesinger’s equations III.2.3.1
Second structure connection II.1.1
Semisimple (pre-)Frobenius manifold 1.3.1
Semisimple Euler field 1.2.4
Singularities of meromorphic connections II.2.1
Small quantum multiplication III.5.4.2
Special coordinates of tame semisimple germ III.7.1.1
Special initial conditions II.3.4
Special solutions to Schlesinger’s equations II.3.1.1
Species of algebras IV.6.1.4
Spectral cover of Frobenius manifold III.8.1
Spectrum of Frobenius manifold 1.2.4
Split identity 1.2.1.3 III.7.5.8
Split semisimple (pre-) Frobenius manifold 1.3.1
Stabilization morphism of moduli stacks V.4.4
Stabilization of prestable curve V.1.6
Stabilization of prestable map V.1.7
Stable curve III.2.5
Stable map V. 1.3.2
Stable modular graph III.2.4
STACK V.5.1
Standard weight IV.3.2.1
Strictly special solutions to Schlesinger’s equations II.3.1.3
String equation VI.5.2
Structure connection of pre-Frobenius manifold 1.1.4
Supermanifold I.1.1.1
Tame semisimple germ of Frobenius manifold III.7.1
Tame singularity of a connection II.2.1
Tau-function of solution II.2.3.2
Tensor product diagram III.7.5.9
Tensor product of analytic Frobenius manifolds III.7
Tensor product of formal Frobenius manifolds III.4.4 III.4.10 III.6.6
Theta-divisor of Schlesinger’s equations II.2.3
Twisted Frobenius manifold 1.5.4.2
Unfolding singularities III.8.4
Versal deformation of meromorphic connection II.2.2
Vertex (of graph) III.2.1
Virasoro constraints Vl.2.5 VI.5
Virtual dimension V.1.9
Virtual fundamental class VI.1.1
Virtual Poincare polynomial IV.4.1
WDW-equations (= associativity equations) 1.1.3.1 1.1.9
Weak Euler field 1.5.4.2
Weak Frobenius manifold 1.5.3
Weight of Euler field III.4.10
Weight of identity III.4.10
Weight of weak Euler field 1.5.4.2
Weil — Petersson volumes III.6.4
Wick’s lemma IV.3.4.2
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