136 citations · 136 across the 7 of their papers we have counts for
8 papers
Geometric quantization for proper moment maps: the Vergne conjecture
Xiaonan Ma, Weiping Zhang
We establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map.
Bergman kernels and symplectic reduction
Xiaonan Ma, Weiping Zhang
We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic ident…
Superconnection and family Bergman kernels
Xiaonan Ma, Weiping Zhang
We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem.
η-invariant and flat vector bundles II
Xiaonan Ma, Weiping Zhang
We first apply the method and results in the previous paper to give a new proof of a result (hold in ) of Gilkey on the variation of h-invariants associated to no…
-invariant and flat vector bundles
Xiaonan MA, Weiping Zhang
We present an alternate definition of the mod {\bf Z} component of the Atiyah-Patodi-Singer invariant associated to (not necessary unitary) flat vector bundles, which identifie…
Eta-invariants, Torsion forms and Flat vector bundles
Xiaonan Ma, weiping Zhang
We present a new proof, as well as a extension, of the Riemann-Roch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The main techniques used are the comput…