Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The de Rham-Federer Theory of Differential Characters and Character
  Duality   The theory of differential characters is developed completely from a de Rham
- Federer viewpoint. Characters are defined as equivalence classes of special
currents, called sparks, which appear naturally in the theory of singular
connections. There are many different spaces of currents which yield the
character groups. A multiplication of de Rham-Federer characters is defined
using transversality results for flat and rectifiable currents. There is a
natural equivalence of ring functors from deRham - Federer characters to
Cheeger-Simons characters. Differential characters have a topology and natural
smooth Pontrjagin duals (introduced here). A principal result is the
formulation and proof of duality for characters on oriented manifolds. It is
shown that the pairing (a,b) --> a*b([X]) given by multiplication and
evaluation on the fundamental cycle, gives an isomorphism of the group of
differential characters of degree k with the dual to characters in degree n-k-1
where n = dim(X). It is also shown that there are natural Thom homomorphisms
for differential characters. Gysin maps are also defined for differential
characters. Many examples including Morse sparks, Hodge sparks and
characteristic sparks are examined in detail.

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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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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: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat