Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomological rigidity of manifolds defined by right-angled
  3-dimensional polytopes   A family of closed manifolds is called cohomologically rigid if a cohomology
ring isomorphism implies a diffeomorphism for any two manifolds in the family.
We establish cohomological rigidity for large families of 3-dimensional and
6-dimensional manifolds defined by 3-dimensional polytopes.
  We consider the class P of 3-dimensional combinatorial simple polytopes,
different from a tetrahedron, whose facets do not form 3- and 4-belts. This
class includes mathematical fullerenes, i.e. simple 3-polytopes with only
5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope from P
admits a right-angled realisation in Lobachevsky 3-space, which is unique up to
isometry.
  Our families of smooth manifolds are associated with polytopes from the class
P. The first family consists of 3-dimensional small covers of polytopes from P,
or hyperbolic 3-manifolds of Loebell type. The second family consists of
6-dimensional quasitoric manifolds over polytopes from P. Our main result is
that both families are cohomologically rigid, i.e. two manifolds M and M' from
either of the families are diffeomorphic if and only if their cohomology rings
are isomorphic. We also prove that if M and M' are diffeomorphic, then their
corresponding polytopes are combinatorially equivalent. These results are
intertwined with the classical subjects of geometry and topology, such as
combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds,
diffeomorphism classification of 6-manifolds and invariance of Pontryagin
classes. The proofs use techniques of toric topology.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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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: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th