Etale groupoids arising from products of shifts of finite type
By H. Matui. 2015
65 citations recorded by the source corpus.
Two conjectures about homology groups, K-groups and topological full groups of minimal etale groupoids on Cantor sets are formulated. We verify these conjectures for many examples of etale groupoids including products of etale groupoids arising from one-sided shifts of finite type. Furthermore, we completely determine when these product groupoids are mutually isomorphic. Also, the abelianization of their topological full groups are computed. They are viewed as generalizations of the higher dimensional Thompson groups.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/600a9e47014d6a9cd6266bd9c15386007c5a2c8b
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In Algebra and Number Theory
- Aidan Sims
- David Pask
- Alex Kumjian
- Carla Farsi
- Volodymyr V. Nekrashevych
- R. Exel
- Trent Yeend
- Enrique Pardo
In Mathematical Physics
- Aidan Sims
- David Pask
- Alex Kumjian
- Carla Farsi
- Volodymyr V. Nekrashevych
- R. Exel
- Enrique Pardo
- Trent Yeend
Citations in the corpus
- Simple groups of dynamical origin (2015, background): “Other examples of the cases when the epimorphism H0(G, Z/2Z)−→ S(G)/A(G) is not an isomorphism are described in [21].”
- Ample groupoids: equivalence, homology, and Matui's HK conjecture (2018, background): “In a series of recent papers [32, 33, 34], Matui has advanced a conjecture that if G is a minimal effective ample Hausdorff groupoid with compact unit space then K0(C ∗ r (G)) is isomorphic to the direct sum of the even homology groups H2n(G) of the groupoid as defined by Crainic and Moerdijk [11], ”