Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The norm of the Euler class   We prove that the norm of the Euler class E for flat vector bundles is
$2^{-n}$ (in even dimension $n$, since it vanishes in odd dimension). This
shows that the Sullivan--Smillie bound considered by Gromov and Ivanov--Turaev
is sharp. We construct a new cocycle representing E and taking only the two
values $\pm 2^{-n}$; a null-set obstruction prevents any cocycle from existing
on the projective space. We establish the uniqueness of an antisymmetric
representative for E in bounded cohomology.

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The categories of this paper are: q-alg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
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The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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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: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th