Frobenius manifold
WebJan 1, 2004 · Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. … WebThe structure of Frobenius manifolds and its later weakened versions weak Frobenius manifolds, also called F-manifolds, was discovered in the 1980s and 1990s in the process of development and formalisation of Topological Field Theory, including Mirror Conjecture: see [17, 19], and references therein.
Frobenius manifold
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WebThe relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity ... WebSep 1, 2024 · We derive the loop equation from the condition of linearization of actions of the Virasoro symmetries on the tau function, and construct the topological deformation of …
WebJan 4, 2024 · Dubrovin introduced and thoroughly studied in [D] the notion of Frobenius manifold. By definition, it is a structure (M, g, ) where M is a manifold, is an associative, commutative and OM ... WebAbstract. In these lectures, some of the geometrical themes in the work of Boris Dubrovin on Frobenius manifolds are discussed. We focus principally on those aspects which have a symplectic flavour, including …
WebFeb 1, 2011 · In mathematics Frobenius manifolds arise in two different situations, corresponding to A-models and B-models in physics. In an A-model one counts rational curves on a variety; this is also known as Gromov–Witten invariants. The generating function for these invariants is the potential for the corresponding Frobenius manifold. Web2. The Frobenius Theorem It turns out that the Frobenius condition is not only necessary but also su cient for a distri-bution to be integrable. Theorem 2.1 (Global Frobenius Theorem). Let Vbe an involutive k-dimensional distribution. Then through every point p2M, there is a unique maximal connected integral manifold of V. Example.
WebNov 6, 2024 · A Dubrovin-Frobenius manifold structure of NLS type on the orbit space of. Generalizing a construction presented in [3], we show that the orbit space of less the image of coordinate lines under the quotient map is equipped with two Dubrovin-Frobenius manifold structures which are related respectively to the defocusing and the focusing …
WebModuli of Semisimple Frobenius Manifolds. All n-dimensional semisimple Frobenius manifolds form a finite-dimensional space. They depend on n(n−1)/2 essential parameters. To parametrize the Frobenius manifolds one can choose, for example, the initial data for the isomonodromy deformation equations [24]. Alternatively, they can be parametrized ... busfamWebA geometric structure called a Frobenius manifold was introduced by Dubrovin to encode such information. It forms the foundation of some reconstruction approaches and plays the role of fundamental laws of individual particles. Two formalisms have been proposed to reconstruct the whole theory from a Frobenius manifold, under a technical ... bus fare and sky train fareIn the mathematical field of differential geometry, a Frobenius manifold, introduced by Dubrovin, is a flat Riemannian manifold with a certain compatible multiplicative structure on the tangent space. The concept generalizes the notion of Frobenius algebra to tangent bundles. Frobenius manifolds … See more Let M be a smooth manifold. An affine flat structure on M is a sheaf T of vector spaces that pointwisely span TM the tangent bundle and the tangent bracket of pairs of its sections vanishes. As a local example … See more The associativity of the product * is equivalent to the following quadratic PDE in the local potential Φ where Einstein's … See more Beside Frobenius algebras, examples arise from quantum cohomology. Namely, given a semipositive symplectic manifold (M, ω) then there … See more bus fare arena fortniteWebFrobenius manifolds have emerged in a wide range of contexts, e.g. singularity theory, quantum cohomology and complex structure moduli spaces of Calabi-Yau varieties. Manin, Hertling and others recognized that the concept of … bus fare assistancehttp://staff.ustc.edu.cn/~wangzuoq/Courses/16F-Manifolds/Notes/Lec11.pdf handbuff paladin wildWebBanach manifolds. The infinite-dimensional version of the Frobenius theorem also holds on Banach manifolds. The statement is essentially the same as the finite-dimensional version. Let M be a Banach manifold of class at least C 2. Let E be a subbundle of the tangent bundle of M. hand buff a carWebMar 8, 2024 · Theorem 1 (Main theorem). The fourth F-manifold has the following properties: . 1. It is identified to a projective manifold, defined over the rank two Frobenius algebra \(\mathfrak {A}\).. 2. The fourth F-manifold decomposes into a pair of isomorphic totally geodesic submanifolds Footnote 1, respectively equipped with a flat connection … hand buffing