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The chern character of semifinite spectral triples

Journal Article


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Abstract


  • In previous work we generalised both the odd and even local index formula of Connes and

    Moscovici to the case of spectral triples for a ∗-subalgebra A of a general semifinite von Neumann

    algebra. Our proofs are novel even in the setting of the original theorem and rely on

    the introduction of a function valued cocycle (called the resolvent cocycle) which is ‘almost’ a

    (b,B)-cocycle in the cyclic cohomology of A. In this paper we show that this resolvent cocycle

    ‘almost’ represents the Chern character, and assuming analytic continuation properties for zeta

    functions, we show that the associated residue cocycle, which appears in our statement of the

    local index theorem does represent the Chern character.

Publication Date


  • 2008

Citation


  • Carey, A. L., Phillips, J., Rennie, A. C. & Sukochev, F. A. (2008). The chern character of semifinite spectral triples. Journal of Noncommutative Geometry, 2 (2), 253-283.

Scopus Eid


  • 2-s2.0-84857290803

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1634&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/628

Number Of Pages


  • 30

Start Page


  • 253

End Page


  • 283

Volume


  • 2

Issue


  • 2

Abstract


  • In previous work we generalised both the odd and even local index formula of Connes and

    Moscovici to the case of spectral triples for a ∗-subalgebra A of a general semifinite von Neumann

    algebra. Our proofs are novel even in the setting of the original theorem and rely on

    the introduction of a function valued cocycle (called the resolvent cocycle) which is ‘almost’ a

    (b,B)-cocycle in the cyclic cohomology of A. In this paper we show that this resolvent cocycle

    ‘almost’ represents the Chern character, and assuming analytic continuation properties for zeta

    functions, we show that the associated residue cocycle, which appears in our statement of the

    local index theorem does represent the Chern character.

Publication Date


  • 2008

Citation


  • Carey, A. L., Phillips, J., Rennie, A. C. & Sukochev, F. A. (2008). The chern character of semifinite spectral triples. Journal of Noncommutative Geometry, 2 (2), 253-283.

Scopus Eid


  • 2-s2.0-84857290803

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1634&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/628

Number Of Pages


  • 30

Start Page


  • 253

End Page


  • 283

Volume


  • 2

Issue


  • 2