ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS

Yi, In-Hyeop; Yi, In-Hyeop

doi:10.7468/jksmeb.2011.18.2.141

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2011, v.18 no.2, pp.141-155

https://doi.org/10.7468/jksmeb.2011.18.2.141

Yi, In-Hyeop

Yi,, I. (2011). ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 18(2), 141-155, https://doi.org/10.7468/jksmeb.2011.18.2.141

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Abstract

We compute zeta functions of 1-solenoids. When our 1-solenoid is nonorientable, we compute Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid and its orientable double cover explicitly in terms of adjacency matrices and branch points. And we show that Artin-Mazur zeta function of orientable double cover is a rational function and a quotient of Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid.

keywords: generalized solenoid, Artin-Mazur zeta function, Lefschetz zeta function, Lefschetz number

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Article Contents

Vol.18 No.2

ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS

Abstract

Reference

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics