27 citations · 55 across the 11 of their papers we have counts for
11 papers
Integral-integral affine geometry, geometric quantization, and Riemann-Roch
Mark Hamilton, Yael Karshon, Takahiko Yoshida
We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann-Roch number coincides with its number of Bohr-Sommerfeld…
Adiabatic Limit, Theta Function, and Geometric Quantization
Takahiko Yoshida
Let be a non-singular Lagrangian torus fibration on a complete base with prequantum line bundle . Compactness on is no…
The equivariant local index of the reduced space in the symplectic cutting
Takahiko Yoshida
We compute the equivariant local index for the reduced space in a symplectic cut space, provided that the reduced space is compact.
Geodesic flows on spheres and the local Riemann-Roch numbers
Hajime Fujita, Mikio Furuta, Takahiko Yoshida
We calculate the local Riemann-Roch numbers of the zero sections of and , where the local Riemann-Roch numbers are defined by using the -bundle structure o…
Equivariant local index
Takahiko Yoshida
This is an expository article on the equivariant local index developed by Fujita, Furuta, and the author in arXiv:1008.5007.
Torus fibrations and localization of index III
Hajime Fujita, Mikio Furuta, Takahiko Yoshida
This paper is the third of the series concerning the localization of the index of Dirac-type operators. In our previous papers we gave a formulation of index of Dirac-type operator…
Torus fibrations and localization of index II
Hajime Fujita, Mikio Furuta, Takahiko Yoshida
We give a framework of localization for the index of a Dirac-type operator on an open manifold. Suppose the open manifold has a compact subset whose complement is covered by a fami…
Torus fibrations and localization of index I
Hajime Fujita, Mikio Furuta, Takahiko Yoshida
We define a local Riemann-Roch number for an open symplectic manifold when a complete integrable system without Bohr-Sommerfeld fiber is provided on its end. In particular when a s…
On Liftings of Local Torus Actions to Fiber Bundles
Takahiko Yoshida
In this note we define a lifting of a local torus action modeled on the standard representation (we call it a local torus action for simplicity) to a principal torus bundle, and sh…
Local torus actions modeled on the standard representation
Takahiko Yoshida
We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standa…
Twisted toric structures
Takahiko Yoshida
This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem…