Homology and AH conjecture for groupoids on one-dimensional solenoids

Inhyeop Yi

doi:10.1016/j.exmath.2022.08.002

Homology and AH conjecture for groupoids on one-dimensional solenoids

Inhyeop Yi

Department of Mathematics Education

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

Abstract

We show that Matui's AH conjecture holds for groupoids of the Bratteli–Vershik systems embedded in the unstable equivalence relation on one-dimensional solenoids.

Original language	English
Pages (from-to)	1084-1095
Number of pages	12
Journal	Expositiones Mathematicae
Volume	40
Issue number	4
DOIs	https://doi.org/10.1016/j.exmath.2022.08.002
State	Published - Dec 2022

Bibliographical note

Funding Information:
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT ( NRF-2021R1F1A106314011 ).

Publisher Copyright:
© 2022 The Author(s)

Keywords

AH-conjecture
Bratteli–Vershik system
Homology groups
One-dimensional solenoid
Topological full group

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10.1016/j.exmath.2022.08.002

Cite this

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title = "Homology and AH conjecture for groupoids on one-dimensional solenoids",

abstract = "We show that Matui's AH conjecture holds for groupoids of the Bratteli–Vershik systems embedded in the unstable equivalence relation on one-dimensional solenoids.",

keywords = "AH-conjecture, Bratteli–Vershik system, Homology groups, One-dimensional solenoid, Topological full group",

author = "Inhyeop Yi",

note = "Funding Information: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT ( NRF-2021R1F1A106314011 ). Publisher Copyright: {\textcopyright} 2022 The Author(s)",

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N1 - Funding Information: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT ( NRF-2021R1F1A106314011 ). Publisher Copyright: © 2022 The Author(s)

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AB - We show that Matui's AH conjecture holds for groupoids of the Bratteli–Vershik systems embedded in the unstable equivalence relation on one-dimensional solenoids.

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KW - Bratteli–Vershik system

KW - Homology groups

KW - One-dimensional solenoid

KW - Topological full group

UR - https://www.scopus.com/pages/publications/85141991847

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JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 4

ER -

Homology and AH conjecture for groupoids on one-dimensional solenoids

Abstract

Bibliographical note

Keywords

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