Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909738597351424 |
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| author | Proietti, Valerio Yamashita, Makoto |
| author_facet | Proietti, Valerio Yamashita, Makoto |
| contents | We study homological invariants of étale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology groups defined by Putnam are isomorphic to the Crainic-Moerdijk groupoid homology with integer coefficients. We also show that the K-groups of C*-algebras of stable and unstable equivalence relations have finite rank. For unstably disconnected Smale spaces, we provide a cohomological spectral sequence whose second page is the (stable) homology groups, and converges to the K-groups of the unstable C*-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03118 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces Proietti, Valerio Yamashita, Makoto K-Theory and Homology Dynamical Systems Operator Algebras 37B02, 55T25, 46L80 We study homological invariants of étale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology groups defined by Putnam are isomorphic to the Crainic-Moerdijk groupoid homology with integer coefficients. We also show that the K-groups of C*-algebras of stable and unstable equivalence relations have finite rank. For unstably disconnected Smale spaces, we provide a cohomological spectral sequence whose second page is the (stable) homology groups, and converges to the K-groups of the unstable C*-algebra. |
| title | Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces |
| topic | K-Theory and Homology Dynamical Systems Operator Algebras 37B02, 55T25, 46L80 |
| url | https://arxiv.org/abs/2207.03118 |