Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author: I͡U. I. Manin

Publisher: American Mathematical Soc.

ISBN: 0821874756

Category: Mathematics

Page: 330

View: 241

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.
Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces
Language: en
Pages: 330
Authors: I͡U. I. Manin
Categories: Mathematics
Type: BOOK - Published: - Publisher: American Mathematical Soc.

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
Frobenius Manifolds and Moduli Spaces for Singularities
Language: en
Pages: 292
Authors: Claus Hertling
Categories: Mathematics
Type: BOOK - Published: 2002-07-25 - Publisher: Cambridge University Press

This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.
Frobenius Manifolds
Language: en
Pages: 378
Authors: Claus Hertling, Matilde Marcolli
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in Bonn, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and
Isomonodromic Deformations and Frobenius Manifolds
Language: en
Pages: 279
Authors: Claude Sabbah
Categories: Mathematics
Type: BOOK - Published: 2007-12-20 - Publisher: Springer Science & Business Media

Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research
Geometry, Topology, and Mathematical Physics
Language: en
Pages: 338
Authors: V. M. Buchstaber, I. M. Krichever
Categories: Mathematics
Type: BOOK - Published: 2004 - Publisher: American Mathematical Soc.

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