Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delocalized eta invariants, algebraicity, and $K$-theory of group
  $C^*$-algebras   In this paper, we establish a precise connection between higher rho
invariants and delocalized eta invariants. Given an element in a discrete
group, if its conjugacy class has polynomial growth, then there is a natural
trace map on the $K_0$-group of its group $C^\ast$-algebra. For each such trace
map, we construct a determinant map on secondary higher invariants. We show
that, under the evaluation of this determinant map, the image of a higher rho
invariant is precisely the corresponding delocalized eta invariant of Lott. As
a consequence, we show that if the Baum-Connes conjecture holds for a group,
then Lott's delocalized eta invariants take values in algebraic numbers. We
also generalize Lott's delocalized eta invariant to the case where the
corresponding conjugacy class does not have polynomial growth, provided that
the strong Novikov conjecture holds for the group.

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The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
3
The categories of this paper are: physics