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SUB-SIGNATURE OPERATORS,η-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES 被引量：1

SUB-SIGNATURE OPERATORS,η-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES
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摘要 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.
作者 ZHANGWEIPING
机构地区 NankaiInstituteofMathematics
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2004年第1期7-36,共30页 数学年刊（B辑英文版）
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.
关键词 Sub-signature operators η-Invariants Flat vector bundles Riemann-Roch 子符号算子 η-不变量 RIEMANN-ROCH定理 平坦向量丛 定向流形
分类号 O186.12 [理学—基础数学]
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参考文献19

  • 1[1]Atiyah, M. F., Patodi, V. K. & Singer, Ⅰ. M., Spectral asymmetry and Riemannian geometry Ⅰ, Proc.Cambridge Philos. Soc., 77(1975), 43-69.
  • 2[2]Atiyah, M. F., Patodi, V. K. & Singer, Ⅰ. M., Spectral asymmetry and Riemannian geometry Ⅱ, Proc.Cambridge Philos. Soc., 78(1975), 405-432.
  • 3[3]Atiyah, M. F., Patodi, V. K. ＆ Singer, Ⅰ. M., Spectral asymmetry and Riemannian geometry Ⅲ, Proc.Cambridge Philos. Soc., 79(1976), 71-99.
  • 4[4]Atiyah, M. F. ＆ Singer, Ⅰ. M., The index of elliptic operators Ⅴ, Ann. of Math., 93(1971), 139-149.
  • 5[5]Bismut, J. M., The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs, Invent. Math., 83(1986), 91-151.
  • 6[6]Bismut, J. M. & Cheeger, J., η-invariants and their adiabatic limits, J. Amer. Math. Soc., 2(1989),33-70.
  • 7[7]Bismut, J. M. ＆ Cheeger, J., Remarks on the index theorem for families of Dirac operators on manifolds with boundary, in Differential Geometry, B. Lawson and K. Tenenblat (eds.), Longman Scientific, 1992,59-84.
  • 8[8]Bismut, J. M. & Freed, D. S., The analysis of elliptic families Ⅱ: Dirac operators, eta invariants and the holonomy theorem, Comm. Math. Phys., 107(1986), 103-163.
  • 9[9]Bismut, J. M. ＆ Lott, J., Flat vector bundles, direct images and higher real analytic torsion, J. Amer.Math. Soc., 8(1995), 291-363.
  • 10[10]Bismut, J. M. ＆ Zhang, W., An Extension of a Theorem by Cheeger and Muller, Astérisque, No. 205,Paris, 1992.

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Chinese Annals of Mathematics,Series B
2004年 第1期

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