Download E-books J-Holomorphic Curves and Quantum Cohomology (University Lecture) PDF

$J$-holomorphic curves revolutionized the learn of symplectic geometry whilst Gromov first brought them in 1985. via quantum cohomology, those curves at the moment are associated with a few of the most fun new principles in mathematical physics. This booklet provides the 1st coherent and whole account of the idea of $J$-holomorphic curves, the main points of that are almost immediately scattered in a variety of examine papers. the 1st 1/2 the booklet is an expository account of the sphere, explaining the most technical elements. McDuff and Salamon supply whole proofs of Gromov's compactness theorem for spheres and of the life of the Gromov-Witten invariants. the second one half the booklet makes a speciality of the definition of quantum cohomology. The authors identify that this multiplication exists, and provides a brand new facts of the Ruan-Tian consequence that's associative on acceptable manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, resulting in quantum Chern sessions and Witten's calculation for Grassmannians, which pertains to the Verlinde algebra. The Dubrovin connection, Gromov-Witten strength on quantum cohomology, and curve counting formulation also are mentioned. The publication closes with an overview of connections to Floer conception.

Show description

Read Online or Download J-Holomorphic Curves and Quantum Cohomology (University Lecture) PDF

Best Differential Geometry books

Differential Geometry (Dover Books on Mathematics)

An introductory textbook at the differential geometry of curves and surfaces in 3-dimensional Euclidean area, offered in its easiest, such a lot crucial shape, yet with many explanatory information, figures and examples, and in a way that conveys the theoretical and sensible value of different innovations, tools and effects concerned.

Variational Problems in Differential Geometry (London Mathematical Society Lecture Note Series, Vol. 394)

The sphere of geometric variational difficulties is fast-moving and influential. those difficulties engage with many different components of arithmetic and feature robust relevance to the research of integrable structures, mathematical physics and PDEs. The workshop 'Variational difficulties in Differential Geometry' held in 2009 on the collage of Leeds introduced jointly across the world revered researchers from many various components of the sector.

Lie Algebras, Geometry, and Toda-Type Systems (Cambridge Lecture Notes in Physics)

Dedicated to a massive and well known department of contemporary theoretical and mathematical physics, this publication introduces using Lie algebra and differential geometry ways to research nonlinear integrable platforms of Toda style. Many difficult difficulties in theoretical physics are concerning the answer of nonlinear structures of partial differential equations.

Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications)

Equipment from touch and symplectic geometry can be utilized to unravel hugely non-trivial nonlinear partial and traditional differential equations with no resorting to approximate numerical tools or algebraic computing software program. This e-book explains how it really is performed. It combines the readability and accessibility of a sophisticated textbook with the completeness of an encyclopedia.

Extra info for J-Holomorphic Curves and Quantum Cohomology (University Lecture)

Show sample text content

Rated 4.98 of 5 – based on 16 votes