Ordered group invariants for nonorientable one-dimensional generalized solenoids

Inhyeop Yi

doi:10.1090/S0002-9939-02-06794-1

Ordered group invariants for nonorientable one-dimensional generalized solenoids

Inhyeop Yi

Department of Mathematics Education

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

2 Scopus citations

Abstract

Let f: X → X be an edge-wrapping rule which presents a one-dimensional generalized solenoid X̄, and let M be the adjacency matrix of f. When X is a wedge of circles and f leaves the unique branch point fixed, we show that the stationary dimension group of M is an invariant of homeomorphism of X̄ even if X̄ is not orientable.

Original language	English
Pages (from-to)	1273-1282
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-02-06794-1
State	Published - Apr 2003

Keywords

One-dimensional generalized solenoid
Ordered group
Orientable double cover

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10.1090/S0002-9939-02-06794-1

Cite this

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title = "Ordered group invariants for nonorientable one-dimensional generalized solenoids",

abstract = "Let f: X → X be an edge-wrapping rule which presents a one-dimensional generalized solenoid {\=X}, and let M be the adjacency matrix of f. When X is a wedge of circles and f leaves the unique branch point fixed, we show that the stationary dimension group of M is an invariant of homeomorphism of {\=X} even if {\=X} is not orientable.",

keywords = "One-dimensional generalized solenoid, Ordered group, Orientable double cover",

author = "Inhyeop Yi",

year = "2003",

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T1 - Ordered group invariants for nonorientable one-dimensional generalized solenoids

AU - Yi, Inhyeop

PY - 2003/4

Y1 - 2003/4

N2 - Let f: X → X be an edge-wrapping rule which presents a one-dimensional generalized solenoid X̄, and let M be the adjacency matrix of f. When X is a wedge of circles and f leaves the unique branch point fixed, we show that the stationary dimension group of M is an invariant of homeomorphism of X̄ even if X̄ is not orientable.

AB - Let f: X → X be an edge-wrapping rule which presents a one-dimensional generalized solenoid X̄, and let M be the adjacency matrix of f. When X is a wedge of circles and f leaves the unique branch point fixed, we show that the stationary dimension group of M is an invariant of homeomorphism of X̄ even if X̄ is not orientable.

KW - One-dimensional generalized solenoid

KW - Ordered group

KW - Orientable double cover

UR - https://www.scopus.com/pages/publications/0037383608

U2 - 10.1090/S0002-9939-02-06794-1

DO - 10.1090/S0002-9939-02-06794-1

M3 - Article

AN - SCOPUS:0037383608

SN - 0002-9939

VL - 131

SP - 1273

EP - 1282

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Ordered group invariants for nonorientable one-dimensional generalized solenoids

Abstract

Keywords

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