Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toeplitz operators and the Roe-Higson type index theorem   Let $M$ be a complete Riemannian manifold and assume that $M$ is partitioned
by a hypersurface $N$. In this paper we introduce a novel class of functions
$C_{\mathrm{w}}(M)$ on noncompact manifolds, which is slightly larger than the
algebra of Higson functions. Out of $\phi$ that belongs to $C_{\mathrm{w}}(M)$
we construct an index class $\mathrm{Ind}(\phi , D)$ in $K_{1}$-group of the
Roe algebra of $M$ by using the Kasparov product. It is supposed to be a
counterpart of Roe's odd index class. We finally prove that Connes' pairing of
$\mathrm{Ind}(\phi , D)$ and Roe's cyclic $1$-cocycle is equal to the Fredholm
index of a Toeplitz operator on $N$. This is an extension of the Roe-Higson
index theorem to even-dimensional partitioned manifold.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph