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A geometric representative for the fundamental class in KK-duality of Smale spaces.
- Source :
-
Journal of Functional Analysis . Jul2024, Vol. 287 Issue 2, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- A fundamental ingredient in the noncommutative geometry program is the notion of KK-duality, often called K-theoretic Poincaré duality, that generalises Spanier-Whitehead duality. In this paper we construct a θ -summable Fredholm module that represents the fundamental class in KK-duality between the stable and unstable Ruelle algebras of a Smale space. To find such a representative, we construct dynamical partitions of unity on the Smale space with highly controlled Lipschitz constants. This requires a generalisation of Bowen's Markov partitions. Along with an aperiodic point-sampling technique we produce a noncommutative analogue of Whitney's embedding theorem, leading to the Fredholm module. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EMBEDDING theorems
*GENERALIZATION
*ALGEBRA
*GEOMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 287
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 177063169
- Full Text :
- https://doi.org/10.1016/j.jfa.2024.110455