A note on the reducibility of automorphisms of the Klein curve and the 𝜂-invariant of mapping tori

Morifuji, Takayuki

doi:10.1090/S0002-9939-98-04297-X

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

Proc. Amer. Math. Soc. 126 (1998), 1945-1947

DOI: https://doi.org/10.1090/S0002-9939-98-04297-X

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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

Michael Atiyah, On framings of $3$-manifolds, Topology 29 (1990), no. 1, 1–7. MR 1046621, DOI 10.1016/0040-9383(90)90021-B
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69. MR 397797, DOI 10.1017/S0305004100049410
Marston Conder, Hurwitz groups: a brief survey, Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 359–370. MR 1041434, DOI 10.1090/S0273-0979-1990-15933-6
I. M. Isaacs, Character theory of finite groups, Academic Press, New York (1990).
Yasushi Kasahara, Reducibility and orders of periodic automorphisms of surfaces, Osaka J. Math. 28 (1991), no. 4, 985–997. MR 1152963
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.
Werner Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973), 239–264 (German). MR 331382, DOI 10.1007/BF01427946
T. Morifuji, The $\eta$-invariant of mapping tori with finite monodromies, Topology Appl. 75 (1997), 41–49.