Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$-Euler characteristics and the Thurston norm   We assign to a finite $CW$-complex and an element in its first cohomology
group a twisted version of the $L^2$-Euler characteristic and study its main
properties. In the case of an irreducible orientable $3$-manifold with empty or
toroidal boundary and infinite fundamental group we identify it with the
Thurston norm. We will use the $L^2$-Euler characteristic to address the
problem whether the existence of a map inducing an epimorphism on fundamental
groups implies an inequality of the Thurston norms.

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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph