Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tiling spaces are Cantor set fiber bundles   We prove that fairly general spaces of tilings of R^d are fiber bundles over
the torus T^d, with totally disconnected fiber. This was conjectured (in a
weaker form) in [W3], and proved in certain cases. In fact, we show that each
such space is homeomorphic to the d-fold suspension of a Z^d subshift (or
equivalently, a tiling space whose tiles are marked unit d-cubes). The only
restrictions on our tiling spaces are that 1) the tiles are assumed to be
polygons (polyhedra if d>2) that meet full-edge to full-edge (or full-face to
full-face), 2) only a finite number of tile types are allowed, and 3) each tile
type appears in only a finite number of orientations. The proof is
constructive, and we illustrate it by constructing a `square' version of the
Penrose tiling system.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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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: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio