Adiabatic limits of η-invariants and the Meyer functions

被引：0
作者：
Shuichi Iida
机构：
来源：
Mathematische Annalen | 2010年 / 346卷
关键词：
03A60; 12K05; 13L05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We construct a function on the orbifold fundamental group of the moduli space of smooth theta divisors, which we call the Meyer function for smooth theta divisors. In the construction, we use the adiabatic limits of the η-invariants of the mapping torus of theta divisors. We shall prove that the Meyer function for smooth theta divisors cobounds the signature cocycle, and we determine the values of the Meyer function for the Dehn twists. In particular, we give an analytic construction of the Meyer function of genus two.
引用
收藏
页码：669 / 717
页数：48
相关论文
共 41 条
  • [1] Atiyah M.F.(1987)Logarithm of the Dedekind Math. Ann. 278 335-380
  • [2] Atiyah M.F.(1968)-funktion Ann. Math. 87 546-604
  • [3] Singer I.M.(1991)The index of elliptic operators III Math. Ann. 294 235-265
  • [4] Barge J.(1990)Cocycle d’Euler et de Maslov Acta Math. 165 1-103
  • [5] Ghys E.(1989)Fiberés déterminants, métriques de Quillen et dégénérescence des courbes J. Am. Math. Soc. 2 33-70
  • [6] Bismut J.-M.(1992)-Invariants and their adiabatic limits Ann. Sci. École Norm. Sup. 25 335-391
  • [7] Bost J.-B(1986)Transgressed of Euler class of Comm. Math. Phys. 106 159-176
  • [8] Bismut J.-M.(1988) vector bundles, adiabatic limits of eta invariants and special values of Comm. Math. Phys. 115 49-78
  • [9] Cheeger J.(1968)-functions Acta Math. 114 71-112
  • [10] Bismut J.-M.(1957)The analysis of elliptic families I: Metrics and connections on determinant bundles, II: Dirac operators, eta invariants, and the holonomy theorem of Witten Proc. Am. Math. Soc. 8 587-596
12345