Type invariants for non-abelian odometers
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914974284120064 |
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| author | Hurder, Steven Lukina, Olga |
| author_facet | Hurder, Steven Lukina, Olga |
| contents | In this work, we introduce the type and typeset invariants for equicontinuous group actions on Cantor sets; that is, for generalized odometers. These invariants are collections of equivalence classes of asymptotic Steinitz numbers associated to the action. We show the type is an invariant of the return equivalence class of the action. We introduce the notion of commensurable typesets, and show that two actions which are return equivalent have commensurable typesets. Examples are given to illustrate the properties of the type and typeset invariants. The type and typeset invariants are used to define homeomorphism invariants for solenoidal manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00863 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Type invariants for non-abelian odometers Hurder, Steven Lukina, Olga Dynamical Systems 20E18, 37B05, 37B45, 20K15, 57S10 In this work, we introduce the type and typeset invariants for equicontinuous group actions on Cantor sets; that is, for generalized odometers. These invariants are collections of equivalence classes of asymptotic Steinitz numbers associated to the action. We show the type is an invariant of the return equivalence class of the action. We introduce the notion of commensurable typesets, and show that two actions which are return equivalent have commensurable typesets. Examples are given to illustrate the properties of the type and typeset invariants. The type and typeset invariants are used to define homeomorphism invariants for solenoidal manifolds. |
| title | Type invariants for non-abelian odometers |
| topic | Dynamical Systems 20E18, 37B05, 37B45, 20K15, 57S10 |
| url | https://arxiv.org/abs/2305.00863 |