Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Composition Formula for Asymptotic Morphisms   For graded $C^*$-algebras $A$ and $B$, we construct a semigroup ${\cal
AP}(A,B)$ out of asymptotic pairs. This semigroup is similar to the semigroup
$\Psi(A,B)$ of unbounded KK-modules defined by Baaj and Julg and there is a map
$\Psi(A,B) \to {\cal AP}(A,B)$ when $B$ is stable. Furthermore, there is a
natural semigroup homomorphism ${\cal AP}(A,B) \to E(A,B)$, where $E(A,B)$ is
the E-theory group. We denote the image of this map $E'(A,B)$ and prove both
that $E'(A,B)$ is a group and that the composition product of E-theory
specializes to a composition product on these subgroups. Our main result is a
formula for the composition product on $E'$ under certain operator-theoretic
hypotheses about the asymptotic pairs being composed. This result is
complementary to known results about the Kasparov product of unbounded
KK-modules.

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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph