Lefschetz fixed point formula: Non-isometry case
HTML articles powered by AMS MathViewer
- by Zelin Yi
- Proc. Amer. Math. Soc. 149 (2021), 5393-5406
- DOI: https://doi.org/10.1090/proc/15619
- Published electronically: September 9, 2021
- PDF | Request permission
Abstract:
In this note, we give a geometric proof of the Lefschetz fixed point formula for not-necessarily isometric map. The proof uses a modified Getzler rescaling and the associated rescaled bundle construction (Higson and Yi [Doc. Math. 24 (2019), pp. 1677–1720]).References
- Nicole Berline, Ezra Getzler, and Michèle Vergne, Heat kernels and Dirac operators, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 298, Springer-Verlag, Berlin, 1992. MR 1215720, DOI 10.1007/978-3-642-58088-8
- Francis Bischoff, Henrique Bursztyn, Hudson Lima, and Eckhard Meinrenken, Deformation spaces and normal forms around transversals, Compos. Math. 156 (2020), no. 4, 697–732. MR 4065067, DOI 10.1112/s0010437x1900784x
- Jean-Michel Bismut and Weiping Zhang, An extension of a theorem by Cheeger and Müller, Astérisque 205 (1992), 235 (English, with French summary). With an appendix by François Laudenbach. MR 1185803
- Ahmad Reza Haj Saeedi Sadegh and Nigel Higson, Euler-like vector fields, deformation spaces and manifolds with filtered structure, Doc. Math. 23 (2018), 293–325. MR 3846057, DOI 10.4171/dm/619
- Nigel Higson and Zelin Yi, Spinors and the tangent groupoid, Doc. Math. 24 (2019), 1677–1720. MR 4033830, DOI 10.4171/dm/712
- Matthias Ludewig and Zelin Yi, A short proof of the localization formula for the loop space chern character of spin manifolds, Preprint, arXiv:2010.05892, 2020.
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210112
- Zelin Yi, A groupoid proof of the Lefschetz fixed point formula, J. Geom. Phys. 161 (2021), Paper No. 104036, 8. MR 4184668, DOI 10.1016/j.geomphys.2020.104036
- Yan Lin Yu, Local index theorem for signature operators, Acta Math. Sinica (N.S.) 3 (1987), no. 4, 363–372. MR 930766, DOI 10.1007/BF02559916
Bibliographic Information
- Zelin Yi
- Affiliation: School of Mathematical Sciences, Tongji University, Shanghai 200092, People’s Republic of China; and Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
- Email: zelin@tongji.edu.cn
- Received by editor(s): November 2, 2020
- Received by editor(s) in revised form: March 23, 2021, and April 5, 2021
- Published electronically: September 9, 2021
- Communicated by: Guofang Wei
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 5393-5406
- MSC (2020): Primary 58J20
- DOI: https://doi.org/10.1090/proc/15619
- MathSciNet review: 4327441