This is often the 1st monograph devoted to the systematic exposition of the total number of issues on the topic of quantum cohomology. the topic first originated in theoretical physics (quantum string conception) and has persisted to improve generally during the last decade. The author's method of quantum cohomology relies at the proposal of the Frobenius manifold. the 1st a part of the booklet is dedicated to this thought and its vast 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 reports the algebraic geometry mechanisms taken with 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 virtually two hundred examine articles in algebraic geometry, quantity thought, mathematical physics, historical past of tradition, and psycholinguistics. Manin's books, resembling ""Cubic types: Algebra, Geometry, and Arithmetic"" (1974), ""A direction in Mathematical Logic"" (1977), ""Gauge box thought and complicated 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 stable popularity as an outstanding expositor. certainly the current ebook will serve mathematicians for a few years to return.
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