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' 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. This is joint work with Farzad Fathizadeh and Franz Luef.

Mathematics

Audience: researchers in the topic

( slides )

Noncommutative Geometry in NYC

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