Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the reducibility
of automorphisms of the Klein curve
and the $\eta$-invariant of mapping tori


Author: Takayuki Morifuji
Journal: Proc. Amer. Math. Soc. 126 (1998), 1945-1947
MSC (1991): Primary 20F05, 57R20; Secondary 57M10, 57S25
DOI: https://doi.org/10.1090/S0002-9939-98-04297-X
MathSciNet review: 1443398
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a characterization for the reducibility of automorphisms of the genus 3 Klein curve in terms of the $\eta$-invariant of finite order mapping tori.


References [Enhancements On Off] (What's this?)

  • [1] M. F. Atiyah, On framings of 3-manifolds, Topology 29 (1990), 1-7. MR 91g:57025
  • [2] M. F. Atiyah, V. K. Patodi, I. M. Singer, Spectral asymmetry and Riemannian geometry I, Math. Proc. Camb. Phil. Soc. 77 (1975), 43-69. MR 53:1655a
  • [3] M. Conder, Hurwitz groups: A brief survey, Bull. A.M.S. New Ser. 23 (1990), 359-370. MR 91d:20032
  • [4] I. M. Isaacs, Character theory of finite groups, Academic Press, New York (1990). CMP 94:14
  • [5] Y. Kasahara, Reducibility and orders of periodic automorphisms of surfaces, Osaka J. Math. 28 (1991), 985-997. MR 93g:57021
  • [6] A. Matsuura, The automorphism group of the Klein curve in the mapping class group of genus 3, Proc. Japan Acad. 72 Ser. A (1996), 139-140. CMP 97:04
  • [7] W. Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973), 239-264. MR 48:9715
  • [8] T. Morifuji, The $\eta$-invariant of mapping tori with finite monodromies, Topology Appl. 75 (1997), 41-49. CMP 97:05

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20F05, 57R20, 57M10, 57S25

Retrieve articles in all journals with MSC (1991): 20F05, 57R20, 57M10, 57S25


Additional Information

Takayuki Morifuji
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153, Japan
Email: morifuji@ms406ss5.ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-98-04297-X
Keywords: Klein curve, reducibility, $\eta$-invariant, mapping class group
Received by editor(s): October 15, 1996
Received by editor(s) in revised form: December 20, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society