Reducibility of automorphisms of Hurwitz surfaces and the η-invariant

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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 languageEnglish
Article number1450119
JournalInternational Journal of Mathematics
Volume25
Issue number13
DOIs
Publication statusPublished - 2014 Dec 16

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Keywords

  • Hurwitz surface
  • Macbeath surface
  • automorphism
  • reducibility
  • η-invariant

ASJC Scopus subject areas

  • Mathematics(all)

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