Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spaces of tilings, finite telescopic approximations and gap-labelling   For a large class of tilings, including the Penrose tiling in two dimension
as well as the icosahedral ones in 3 dimension, the continuous hull of such a
tiling inherits a minimal lamination structure with flat leaves and a
transversal which is a Cantor set. In this case, we show that the continuous
hull can be seen as the projective limit of a suitable sequence of branched,
oriented and flat compact manifolds.The algebraic topological features related
to this sequence reflect the dynamical properties of the action on the
continuous hull. In particular the set of positive invariant measures of this
action turns to be a convex cone, canonically associated with the orientation,
in the projective limit of the top homology groups of the branched manifolds.
As an application of this construction we prove a gap-labelling theorem.

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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: solv-int