| Autor: |
Deaconu, Valentin, Ionescu, Marius |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We introduce a cochain complex for ample groupoids $\mathcal G$ using a flat resolution defining their homology with coefficients in $\mathbb Z$. We prove that the cohomology of this cochain complex with values in a $\mathcal G$-module $M$ coincides with the previously introduced continuous cocycle cohomology of $\mathcal G$. In particular, this groupoid cohomology is invariant under Morita equivalence. We derive an exact sequence for the cohomology of skew products by a $\mathbb Z$-valued cocycle. We indicate how to compute the cohomology with coefficients in a $\mathcal G$-module $M$ for $AF$-groupoids and for certain action groupoids. |
| Databáze: |
arXiv |
| Externí odkaz: |
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