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arXiv · 1912.12658

Categorified Fredholm Modules and Chern Characters

Mamta Balodi·Abhishek Banerjee
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Abstract

In this paper, we continue our program of systematic categorification of the Noncommutative Differential Geometry of Connes. We replace a ring with a small $\mathbb C$-linear category, seen as a ring with several objects in the sense of Mitchell. We introduced Fredholm modules over this category and construct a Chern character taking values in the cyclic cohomology of $\mathcal C$. We show that this categorified Chern character depends only on the homotopy class of the Fredholm module and is well-behaved with respect to the periodicity operator in cyclic cohomology.

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Mamta Balodi, Abhishek Banerjee. 2019-12-29. Categorified Fredholm Modules and Chern Characters. https://arxiv.org/abs/1912.12658

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