ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics Education, Ewha Womans University)

Yi, In-Hyeop. (2011). ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS. 한국수학교육학회지시리즈B:순수및응용수학, 18(2), 141-155, https://doi.org/10.7468/jksmeb.2011.18.2.141

복사

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

참고문헌

(2003). . Proc. Amer. Math. Soc., 131, 1273-1282. 10.1090/S0002-9939-02-06794-1.

(1995). . Russian Acad. Sci. Sb. Math., 82, 135-174.

(1974). . IHES Publ. Math., 43, 169-203. 10.1007/BF02684369.

(2001). . Trans. Amer. Math. Soc., 353, 3741-3767. 10.1090/S0002-9947-01-02710-6.

(1978). . Amer. J. Math., 100, 217-243. 10.2307/2373849.

(1967). . Topology, 6, 473-487. 10.1016/0040-9383(67)90005-5.

(1970). .

(1967). . Bull. Amer. Math. Soc., 73, 747-817. 10.1090/S0002-9904-1967-11798-1.

10.

11.

(1965). . Ann. of Math., 81, 82-99. 10.2307/1970384.

12.

(2000). . Mem. Amer. Math. Soc., 147(699).

바로가기메뉴

논문 상세

Vol.18 No.2

ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS

ZETA FUNCTIONS FOR ONE-DIMENSIONAL GENERALIZED SOLENOIDS

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학