Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the topology of the Kasparov groups and its applications   In this paper we establish a direct connection between stable approximate
unitary equivalence for $*$-homomorphisms and the topology of the KK-groups
which avoids entirely C*-algebra extension theory and does not require
nuclearity assumptions. To this purpose we show that a topology on the Kasparov
groups can be defined in terms of approximate unitary equivalence for Cuntz
pairs and that this topology coincides with both Pimsner's topology and the
Brown-Salinas topology. We study the generalized R{\o}rdam group
$KL(A,B)=KK(A,B)/\bar{0}$, and prove that if a separable exact residually
finite dimensional C*-algebra satisfies the universal coefficient theorem in
KK-theory, then it embeds in the UHF algebra of type $2^\infty$.
  In particular such an embedding exists for the C*-algebra of a second
countable amenable locally compact maximally almost periodic group.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio