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The K-theory of Heegaard quantum lens spaces

Journal Article


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Abstract


  • Representing Z/NZ as roots of unity, we restrict a natural U(1)-action on the

    Heegaard quantum sphere to Z/NZ, and call the quotient spaces Heegaard quantum lens spaces.

    Then we use this representation of Z/NZ to construct an associated complex line bundle. This

    paper proves the stable non-triviality of these line bundles over any of the quantum lens spaces

    we consider. We use the pullback structure of the C∗-algebra of the lens space to compute

    its K-theory via the Mayer-Vietoris sequence, and an explicit form of the Bass connecting

    homomorphism to prove the stable non-triviality of the bundles. On the algebraic side we

    prove the universality of the coordinate algebra of such a lens space for a particular set of

    generators and relations. We also prove the non-existence of non-trivial invertibles in the

    coordinate algebra of a lens space. Finally, we prolongate the Z/NZ-fibres of the Heegaard

    quantum sphere to U(1), and determine the algebraic structure of such a U(1)-prolongation.

Authors


  •   Hajac, Piotr M. (external author)
  •   Rennie, Adam C.
  •   Zielinski, Bartosz (external author)

Publication Date


  • 2013

Citation


  • Hajac, P. M., Rennie, A. & Zielinski, B. (2013). The K-theory of Heegaard quantum lens spaces. Journal of Noncommutative Geometry, 7 (4), 1185-1216.

Scopus Eid


  • 2-s2.0-84892379443

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2919&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1910

Number Of Pages


  • 31

Start Page


  • 1185

End Page


  • 1216

Volume


  • 7

Issue


  • 4

Abstract


  • Representing Z/NZ as roots of unity, we restrict a natural U(1)-action on the

    Heegaard quantum sphere to Z/NZ, and call the quotient spaces Heegaard quantum lens spaces.

    Then we use this representation of Z/NZ to construct an associated complex line bundle. This

    paper proves the stable non-triviality of these line bundles over any of the quantum lens spaces

    we consider. We use the pullback structure of the C∗-algebra of the lens space to compute

    its K-theory via the Mayer-Vietoris sequence, and an explicit form of the Bass connecting

    homomorphism to prove the stable non-triviality of the bundles. On the algebraic side we

    prove the universality of the coordinate algebra of such a lens space for a particular set of

    generators and relations. We also prove the non-existence of non-trivial invertibles in the

    coordinate algebra of a lens space. Finally, we prolongate the Z/NZ-fibres of the Heegaard

    quantum sphere to U(1), and determine the algebraic structure of such a U(1)-prolongation.

Authors


  •   Hajac, Piotr M. (external author)
  •   Rennie, Adam C.
  •   Zielinski, Bartosz (external author)

Publication Date


  • 2013

Citation


  • Hajac, P. M., Rennie, A. & Zielinski, B. (2013). The K-theory of Heegaard quantum lens spaces. Journal of Noncommutative Geometry, 7 (4), 1185-1216.

Scopus Eid


  • 2-s2.0-84892379443

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2919&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1910

Number Of Pages


  • 31

Start Page


  • 1185

End Page


  • 1216

Volume


  • 7

Issue


  • 4