Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projective Spectrum and Cyclic Cohomolgy   For a tuple $A=(A_1,\ A_2,\ ...,\ A_n)$ of elements in a unital algebra
${\mathcal B}$ over $\mathbb{C}$, its {\em projective spectrum} $P(A)$ or
$p(A)$ is the collection of $z\in \mathbb{C}^n$, or respectively $z\in
\mathbb{P}^{n-1}$ such that the multi-parameter pencil
$A(z)=z_1A_1+z_2A_2+\cdots +z_nA_n$ is not invertible in ${\mathcal B}$.
${\mathcal B}$-valued $1$-form $A^{-1}(z)dA(z)$ contains much topological
information about $P^c(A):=\mathbb{C}^n\setminus P(A)$. In commutative cases,
invariant multi-linear functionals are effective tools to extract that
information. This paper shows that in non-commutative cases, the cyclic
cohomology of ${\mathcal B}$ does a similar job. In fact, a Chen-Weil type map
$\kappa$ from the cyclic cohomology of ${\mathcal B}$ to the de Rham cohomology
$H^*_d(P^c(A),\ \mathbb{C})$ is established. As an example, we prove a closed
high-order form of the classical Jacobi's formula.

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The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph