This is often the 1st monograph devoted to the systematic exposition of the entire number of themes concerning quantum cohomology. the topic first originated in theoretical physics (quantum string thought) and has persevered to boost widely during the last decade. The author's method of quantum cohomology is predicated at the idea of the Frobenius manifold. the 1st a part of the booklet is dedicated to this inspiration and its wide interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. within the moment a part of the booklet, the writer describes the development of quantum cohomology and experiences the algebraic geometry mechanisms enthusiastic about this development (intersection and deformation idea of Deligne-Artin and Mumford stacks).Yuri Manin is at present the director of the Max-Planck-Institut fur Mathematik in Bonn, Germany. He has authored and coauthored 10 monographs and nearly 2 hundred examine articles in algebraic geometry, quantity idea, mathematical physics, historical past of tradition, and psycholinguistics. Manin's books, corresponding to ""Cubic kinds: Algebra, Geometry, and Arithmetic"" (1974), ""A path in Mathematical Logic"" (1977), ""Gauge box idea and intricate Geometry"" (1988), ""Elementary debris: arithmetic, 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 reliable reputation as a very good expositor. definitely the current publication will serve mathematicians for a few years to return.
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