Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal
  Geometry   The aim of the present work is to show how, using the differential calculus
associated to Dirichlet forms, it is possible to construct Fredholm modules on
post critically finite fractals by regular harmonic structures. The modules are
d-summable, the summability exponent d coinciding with the spectral dimension
of the generalized laplacian operator associated with the regular harmonic
structures. The characteristic tools of the noncommutative infinitesimal
calculus allow to define a d-energy functional which is shown to be a
self-similar conformal invariant.

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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: math-ph