Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The perturbation of the de Rham Hodge Operator and the
  Kastler-Kalau-Walze type theorem for manifolds with boundary   In this paper, we give Lichnerowicz type formulas for the perturbation of the
de Rham Hodge operator. We prove the Kastler-Kalau-Walze type theorems for the
perturbation of the de Rham Hodge operator on 4-dimensional and 6-dimensional
compact manifolds with (resp.without) boundary. Some concrete examples of the
perturbation of the de Rham Hodge operator are provided for our main theorems.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an