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The nuclear dimension of C⁎-algebras associated to topological flows and orientable line foliations.
- Source :
-
Advances in Mathematics . Aug2021, Vol. 386, pN.PAG-N.PAG. 1p. - Publication Year :
- 2021
-
Abstract
- We show that for any locally compact Hausdorff space Y with finite covering dimension and for any continuous flow R ↷ Y , the resulting crossed product C ⁎ -algebra C 0 (Y) ⋊ R has finite nuclear dimension. This generalizes previous results for free flows, where this was proved using Rokhlin dimension techniques. As an application, we obtain bounds for the nuclear dimension of C ⁎ -algebras associated to one-dimensional orientable foliations. This result is analogous to the one we obtained earlier for non-free actions of Z. Some novel techniques in our proof include the use of a conditional expectation constructed from the inclusion of a clopen subgroupoid, as well as the introduction of what we call fiberwise groupoid coverings that help us build a link between foliation C ⁎ -algebras and crossed products. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 386
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 151006588
- Full Text :
- https://doi.org/10.1016/j.aim.2021.107798