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  A twisted local index formula for curved noncommutative two tori

Fathizadeh, F., Luef, F., & Tao, J. (submitted). A twisted local index formula for curved noncommutative two tori.

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https://arxiv.org/abs/1904.03810 (Any fulltext)
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 Creators:
Fathizadeh, F1, 2, Author              
Luef, F, Author
Tao, J, Author
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1Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 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' 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.

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 Dates: 2019-04
 Publication Status: Submitted
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