1 citations · 1 across the 4 of their papers we have counts for
12 papers
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…
Eta invariant and Chern-Simons current
Weiping Zhang
We show that the R/Z part of the analytically defined eta invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely…
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…
Modular invariance, characteristic numbers and invariants
Fei Han, Weiping Zhang
We generalize the "miraculous cancellation" formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our…
An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary
Xianzhe Dai, Weiping Zhang
We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singe…
Rigidity and Vanishing Theorems in K-Theory II
Kefeng Liu, Xiaonan Ma, Weiping Zhang
We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1},…