Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse Geometry   Let $A$ be a C*-algebra that is the norm closure $A = \overline{\sum_{\beta
\in \alpha} I_\beta}$ of an arbitrary sum of C*-ideals $I_\beta \subseteq A$.
We construct a homological spectral sequence that takes as input the K-theory
of $\bigcap_{j \in J} I_j$ for all finite nonempty index sets $J \subseteq
\alpha$ and converges strongly to the K-theory of $A$.
  For a coarse space $X$, the Roe algebra $\mathfrak C^* X$ encodes large-scale
properties. Given a coarsely excisive cover $\{X_\beta\}_{\beta \in \alpha}$ of
$X$, we reshape $\mathfrak C^* X_\beta$ as input for the spectral sequence.
From the K-theory of $\mathfrak C^*X \big( \bigcap_{j \in J} X_j \big)$ for
finite nonempty index sets $J \subseteq \alpha$, we compute the K-theory of
$\mathfrak C^* X$ if $\alpha$ is finite, or of a direct limit C*-ideal of
$\mathfrak C^* X$ if $\alpha$ is infinite.
  Analogous spectral sequences exist for the algebra $\mathfrak D^* X$ of
pseudocompact finite-propagation operators that contains the Roe algebra as a
C*-ideal, and for $\mathfrak Q^* X = \mathfrak D^* X / \mathfrak C^* X$.

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The categories of this paper are: stat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph