Gerstenhaber and Batalin-Vilkovisky structures on Lagrangian intersecions
نویسندگان
چکیده
Let M and N be Lagrangian submanifolds of a complex symplectic manifold S. We construct a Gerstenhaber algebra structure on TorS ∗ (OM ,ON ) and a compatible Batalin-Vilkovisky module structure on ExtOS (OM ,ON ). This gives rise to a de Rham type cohomology theory for Lagrangian intersections.
منابع مشابه
Operadic Formulation of Topological Vertex Algebras and Gerstenhaber or Batalin-vilkovisky Algebras
We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak...
متن کاملIdentification of Two Frobenius Manifolds in Mirror Symmetry
We identify two Frobenius manifolds obtained from two different differential Gerstenhaber-Batalin-Vilkovisky (dGBV) algebras on a compact Kähler manifold by Barannikov-Kontsevich-Manin (BKM) construction [1, 13]. One is constructed on the Dolbeault cohomology in Cao-Zhou [5], and the other on the de Rham cohomology in the present paper. This can be considered as a generalization of the identifi...
متن کاملA General Chain Model of the Free Loop Space and String Topology
A chain complex model for the free loop space of a connected compact oriented manifold is presented. Some algebraic operations on such a chain complex are studied, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are proven. The gravity algebra on the equivariant homology of the free loop space is also constructed. This gives an algebraic and chain level model of ...
متن کاملAn Algebraic Chain Model of String Topology
A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology structures. The gravity algebra on the equivariant homology of the free loop space is also modeled. The construction includes the non-simply connected case, and...
متن کاملBatalin–Vilkovisky Integrals in Finite Dimensions
The Batalin-Vilkovisky method (BV ) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangi...
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 2007