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 part...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 η-invariants.展开更多
We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to（not necessary unitary ）flat vector bundles,which identifies explicitly its realandimaginary parts.This...We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to（not necessary unitary ）flat vector bundles,which identifies explicitly its realandimaginary parts.This is done by combining a deformation of flatconnections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah Patodi and Singer.展开更多
基金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.
文摘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 η-invariants.
基金Project supported by the Cheung-Kong Scholarship of the Ministry of Education of Chinathe 973 Project of the Ministry of Science and Technology of China.
文摘We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to（not necessary unitary ）flat vector bundles,which identifies explicitly its realandimaginary parts.This is done by combining a deformation of flatconnections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah Patodi and Singer.
