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5 papers · 2 filters
Homeomorphism Classification of positively curved manifolds with almost maximal symmetry rank
Fuquan Fang, Xiaochun Rong
We show that a closed simply connected 8-manifold (9-manifold) of positive sectional curvature on which a 3-torus (4-torus) acts isometrically is homeomorphic to a sphere, a comple…
Circle actions and Z/k-manifolds
Weiping Zhang
We establish an S^1-equivariant index theorem for Dirac operators on Z/k-manifolds. As an application, we generalize the Atiyah-Hirzebruch vanishing theorem for S^1-actions on clos…
Heat kernels and the index theorems on even and odd dimensional manifolds
Weiping Zhang
In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for D…
Index iteration theory for symplectic paths with applications to nonlinear Hamiltonian systems
Yiming Long
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. Th…
Holomorphic Equivariant Cohomology via a Transversal Holomorphic Vector Field
Huitao Feng
In this paper an analytic proof of a generalization of a theorem of Bismut ([Bis1, Theorem 5.1]) is given, which says that, when is a transversal holomorphic vector field on a…