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Miscellaneous 2019

A twisted local index formula for curved noncommutative two tori

{We consider the Dirac operator of a general metric in the canonical conformal class on the noncommutative two torus, twisted by an idempotent (representing the K-theory class of a general noncommutative vector bundle), and derive a local formula for the Fredholm index of the twisted Dirac operator. Our approach is based on the McKean-Singer index formula, and explicit heat expansion calculations by making use of Connes\textquotesingle pseudodifferential calculus. As a technical tool, a new rearrangement lemma is proved to handle challenges posed by the noncommutativity of the algebra and the presence of an idempotent in the calculations in addition to a conformal factor.}

Author(s): Fathizadeh, F and Luef, F and Tao, J
Year: 2019
Bibtex Type: Miscellaneous (misc)
Electronic Archiving: grant_archive

BibTex 

@misc{item_3047905,
  title = {{A twisted local index formula for curved noncommutative two tori}},
  abstract = {{We consider the Dirac operator of a general metric in the canonical conformal class on the noncommutative two torus, twisted by an idempotent (representing the K-theory class of a general noncommutative vector bundle), and derive a local formula for the Fredholm index of the twisted Dirac operator. Our approach is based on the McKean-Singer index formula, and explicit heat expansion calculations by making use of Connes\textquotesingle pseudodifferential calculus. As a technical tool, a new rearrangement lemma is proved to handle challenges posed by the noncommutativity of the algebra and the presence of an idempotent in the calculations in addition to a conformal factor.}},
  year = {2019},
  slug = {item_3047905},
  author = {Fathizadeh, F and Luef, F and Tao, J}
}