Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An interesting example for spectral invariants   In "Illinois J. of Math. {\bf 38} (1994) 653--678", the heat operator of a
Bismut superconnection for a family of generalized Dirac operators is defined
along the leaves of a foliation with Hausdorff groupoid. The Novikov-Shubin
invariants of the Dirac operators were assumed greater than three times the
codimension of the foliation. It was then showed that the associated heat
operator converges to the Chern character of the index bundle of the operator.
In "J. K-Theory {\bf 1} (2008) 305--356", we improved this result by reducing
the requirement on the Novikov-Shubin invariants to one half of the
codimension. In this paper, we construct examples which show that this is the
best possible result.

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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph