Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative circle bundles and new Dirac operators   We study spectral triples over noncommutative principal U(1) bundles. Basing
on the classical situation and the abstract algebraic approach, we propose an
operatorial definition for a connection and compatibility between the
connection and the Dirac operator on the total space and on the base space of
the bundle. We analyze in details the example of the noncommutative three-torus
viewed as a U(1) bundle over the noncommutative two-torus and find all
connections compatible with an admissible Dirac operator. Conversely, we find a
family of new Dirac operators on the noncommutative tori, which arise from the
base-space Dirac operator and a suitable connection.

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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
9
The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc