56 citations · 642 across the 79 of their papers we have counts for
18 papers · 1 filter
Hessian Geometry and Phase Changes of Multi-Taub-NUT Metrics
Jian Zhou
We study the Hessian geometry of toric multi-Taub-NUT metrics and their phase change phenomena via the images of their moment maps. This generalizes an earlier paper on toric Gibbo…
Hessian Geometry and Phase Change of Gibbons-Hawking Metrics
Jian Zhou
We study the Hessian geometry of toric Gibbons-Hawking metrics and their phase change phenomena via the images of their moment maps.
-theory associated to vertex operator algebras
Chongying Dong, Kefeng Liu, Xiaonan Ma +1
We introduce two -theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algeb…
Superconformal vertex algebras in differential geometry. I
Jian Zhou
We show how to construct an N=1 superconformal vertex algebra (SCVA) from any Riemannian manifold. When the Riemannian manifold has special holonomy groups, we discuss the extended…
DGBV Algebras and Mirror Symmetry
Huai-Dong Cao, Jian Zhou
We describe some recent development on the theory of formal Frobenius manifolds via a construction from differential Gerstenhaber-Batalin-Vilkovisk (DGBV) algebras and formulate a…
Calculations of the Hirzebruch genera of symmetric products by the holomorphic Lefschetz formula
Jian Zhou
We calculate the Hirzebruch and -genera of symmetric products of closed complex manifolds by the holomorphic Lefschetz formula of Atiyah and Singer \cite{Ati-Sin}. S…
Delocalized equivariant coholomogy of symmetric products
Jian Zhou
For any closed complex manifold , we calculate the Poincaré and Hodge polynomials of the delocalized equivariant cohomology with a grading specified by physicist…
Rational homotopy types of mirror manifolds
Jian Zhou
We explain how to relate the problem of finding a mirror manifold for a Calabi-Yau manifold to the problem of characterizing the rational homotopy types of closed Kähler manifolds.
Homological perturbation theory and mirror symmetry
Jian Zhou
We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poiss…
On quasi-isomorphic DGBV algebras
Huai-Dong Cao, Jian Zhou
One of the methods to obtain Frobenius manifold structures is via DGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebra construction. An important problem is how to identify…
Hodge theory and structures on cohomology
Jian Zhou
We use Hodge theory and a construction of Merkulov to construct structures on de Rham cohomology and Dolbeault cohomology.
Formal Frobenius manifold structure on equivariant cohomology
Huai-Dong Cao, Jian Zhou
For a closed Kähler manifold with a Hamiltonian action of a connected compact Lie group by holomorphic isometries, we construct a formal Frobenius manifold structure on the equivar…
On Quantum de Rham Cohomology
Huai-Dong Cao, Jian Zhou
We define quantum exterior product wedge_h and quantum exterior differential d_h on Poisson manifolds, of which symplectic manifolds are an important class of examples. Quantum de…
Identification of Two Frobenius Manifolds In Mirror Symmetry
Huai-Dong Cao, Jian Zhou
We identify two Frobenius manifolds obtained from two different differential Gerstenhaber-Batalin-Vilkovisky algebras on a compact Kaehler manifold. One is constructed on the Dolbe…
Frobenius Manifold Structure on Dolbeault Cohomology and Mirror Symmetry
Huai-Dong Cao, Jian Zhou
We construct a differential Gerstenhaber-Batalin-Vilkovisky algebra from Dolbeault complex of any close Kaehler manifold, and a Frobenius manifold structure on Dolbeault cohomology…
On Quantum de Rham Cohomology Theory
Huai-Dong Cao, Jian Zhou
We define quantum exterior product wedge_h and quantum exterior differential d_h on Poisson manifolds (of which symplectic manifolds are an important class of examples). Quantum de…
Equivariant Cohomology and Wall Crossing Formulas in Seiberg-Witten Theory
Huai-Dong Cao, Jian Zhou
We use localization formulas in the theory of equivariant cohomology to rederive the wall crossing formulas of Li-Liu and Okonek-Teleman for Seiberg-Witten invariants.
Degenerate Chern-Weil Theory and Equivariant Cohomology
Huai-Dong Cao, Jian Zhou
We develop a Chern-Weil theory for compact Lie group action whose generic stabilizers are finite in the framework of equivariant cohomology. This provides a method of changing an e…