Extended Cohomological Field Theories and Noncommutative Frobenius Manifolds
نویسنده
چکیده
We construct an extension (Stable Field Theory) of Cohomological Field Theory. The Stable Field Theory is a system of homomorphisms to some algebras generated by spheres and disks with punctures. It is described by a formal tensor series, satisfying to some system of ”differential equations”. In points of convergence the tensor series generate special noncommutative analogs of Frobenius algebras, describing ’Open-Closed’ Topological Field
منابع مشابه
Extention Cohomological Fields Theory and Noncommutative Frobenius Manifolds
INTRODUCTION The Cohomological Field Theory was propose by Kontsevich and Manin [5] for description of Gromov-Witten Classes. They prove that Cohomological Field Theory is equivalent to Formal Frobenius manifold. Formal Frobenius manifold is defined by a formal series F , satisfying to associative equations. In points of convergence the series F defines a Frobenius algebras. The set of these po...
متن کاملNoncommutative Cohomological Field Theories and Topological Aspects of Matrix models
We study topological aspects of matrix models and noncommutative cohomological field theories (N.C.CohFT). N.C.CohFT have symmetry under the arbitrary infinitesimal noncommutative parameter θ deformation. This fact implies that N.C.CohFT possess a less sensitive topological property than K-theory, but the classification of manifolds by N.C.CohFT has a possibility to give a new view point of glo...
متن کاملQuaternion Landau-ginsburg Models and Noncommutative Frobenius Manifolds
We extend topological Landau-Ginsburg models with boundaries to Quaternion Landau-Ginsburg models that satisfy the axioms for open-closed topological field theories. Later we prove that moduli spaces of Quaternion Landau-Ginsburg models are non-commutative Frobenius manifolds in means of [J. Geom. Phys, 51 (2003),387-403.].
متن کاملPointed Admissible G-covers and G-equivariant Cohomological Field Theories
For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduce to the moduli space of stable curves and a cohomological field theory (CohFT), respectively. We prove that taking the “quotient” by G reduces a G-CohFT to a CohFT. We also prove that a G-CohFT contain...
متن کامل2-dimensional Topological Quantum Field Theories and Frobenius Algebras
Category theory provides a more abstract and thus more general setting for considering the structure of mathematical objects. 2-dimensional quantum field theories arise in physics as objects that assign vector spaces to 1-manifolds and linear maps to 2-cobordisms. From a categorical perspective, we find that they are the same as commutative Frobenius algebras. Our main goal is to explain this e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002