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| SUB-SIGNATURE OPERATORS, $\eta$-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES |
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Citation： |
ZHANG Weiping.SUB-SIGNATURE OPERATORS, $\eta$-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES[J].Chinese Annals of Mathematics B,2004,25(1):7~36 |
| Page view： 1295
Net amount： 855 |
Authors： |
ZHANG Weiping; |
Foundation： |
Project supported by the National Natural Science Foundation of China, the Cheung-Kong Scholarship
of the Ministry of Education of China, the Qiu Shi Foundation and the 973 Project of the Ministry of
Science and Technology of China. |
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| Abstract： |
The author presents an extension of the Atiyah-Patodi-Singer
invariant for unitary representations [2,3] to the non-unitary
case, as well as to the case where the base manifold admits
certain finer structures. In particular, when the base manifold
has a fibration structure, a Riemann-Roch theorem for these
invariants is established by computing the adiabatic limits of the
associated $\eta$-invariants. |
Keywords： |
Sub-signature operators, $\eta$-Invariants, Flat vector bundles, Riemann-Roch |
Classification： |
58J |
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