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Topological Recursion
In mathematics, topological recursion is a recursive definition of invariants of spectral curves. It has applications in enumerative geometry, random matrix theory, mathematical physics, string theory, knot theory. Introduction The topological recursion is a construction in algebraic geometry.Invariants of algebraic curves and topological expansion, B. Eynard, N. Orantin, math-ph/0702045, ccsd-hal-00130963, Communications in Number Theory and Physics, Vol 1, Number 2, p347-452. It takes as initial data a spectral curve: the data of \left(\Sigma,\Sigma_0,x,\omega_,\omega_\right), where: x:\Sigma\to\Sigma_0 is a covering of Riemann surfaces with ramification points; \omega_ is a meromorphic differential 1-form on \Sigma, regular at the ramification points; \omega_ is a symmetric meromorphic bilinear differential form on \Sigma^2 having a double pole on the diagonal and no residue. The topological recursion is then a recursive definition of infinite sequences of symmetric me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
