Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Universality of the Art Gallery Problem   We prove that any compact semi-algebraic set is homeomorphic to the solution
space of some art gallery problem. Previous works have established similar
universality theorems, but holding only up to homotopy equivalence, rather than
homeomorphism, and prior to this work, the existence of art galleries even for
simple spaces such as the M\"obius strip or the three-holed torus were unknown.
Our construction relies on an elegant and versatile gadget to copy guard
positions with minimal overhead, and is thus simpler than previous
constructions, consisting of a single rectangular room with convex slits cut
out from the edges. We additionally show that both the orientable and
non-orientable surfaces of genus $n$ require galleries with only $O(n)$
vertices.

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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: math-ph