The irrational rotation algebra A_θ is known to be Poincaré self-dual in the KK-theoretic sense. The spectral triple representing the required K-homology fundamental class was constructed by Connes out of the Dolbeault operator on the 2-torus, but
so far, there has not been an explicit description of the dual element. We geometrically construct, for certain elements g of the modular group, a finitely generated
projective module L_g over A_θ ⊗ A_θ out of a pair of transverse Kronecker flows on
the 2-torus. For upper triangular g, we find an unbounded cycle representing the
dual of said module under Kasparov product with Connes' class, and prove that this
cycle is invertible in KK(A_θ,A_θ), allowing us to 'untwist' L_g to an unbounded cycle
representing the unit for the self-duality of A_θ. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/11678 |
| Date | 09 April 2020 |
| Creators | Duwenig, Anna |
| Contributors | Emerson, Heath, Laca, Marcelo |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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