Reducibility of automorphisms of Hurwitz surfaces and the η-invariant

Takayuki Morifuji

doi:10.1142/S0129167X14501195

Reducibility of automorphisms of Hurwitz surfaces and the η-invariant

Takayuki Morifuji

Faculty of Economics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we discuss a relationship between the surface symmetry and the spectral asymmetry. More precisely we show that an automorphism of the Macbeath surface of genus 7, or one of the three Hurwitz surfaces of genus 14 is reducible if and only if the η-invariant of the corresponding mapping torus vanishes.

Original language	English
Article number	1450119
Journal	International Journal of Mathematics
Volume	25
Issue number	13
DOIs	https://doi.org/10.1142/S0129167X14501195
Publication status	Published - 2014 Dec 16

Keywords

Hurwitz surface
Macbeath surface
automorphism
reducibility
η-invariant

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0129167X14501195

Cite this

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keywords = "Hurwitz surface, Macbeath surface, automorphism, reducibility, η-invariant",

author = "Takayuki Morifuji",

note = "Funding Information: The author would like to thank anonymous referees for their careful reading of this paper. This study has been partially supported by Grant-in-Aid for Scientific Research (C) 23540076, Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2014 World Scientific Publishing Company.",

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N2 - In this paper, we discuss a relationship between the surface symmetry and the spectral asymmetry. More precisely we show that an automorphism of the Macbeath surface of genus 7, or one of the three Hurwitz surfaces of genus 14 is reducible if and only if the η-invariant of the corresponding mapping torus vanishes.

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KW - Macbeath surface

KW - automorphism

KW - reducibility

KW - η-invariant

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Reducibility of automorphisms of Hurwitz surfaces and the η-invariant

Abstract

Keywords

ASJC Scopus subject areas

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