Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polyhedral surfaces of high genus   The construction of the COMBINATORIAL data for a surface with n vertices of
maximal genus is a classical problem: The maximal genus g=[(n-3)(n-4)/12] was
achieved in the famous ``Map Color Theorem'' by Ringel et al. (1968). We
present the nicest one of Ringel's constructions, for the case when n is
congruent to 7 mod 12, but also an alternative construction, essentially due to
Heffter (1898), which easily and explicitly yields surfaces of genus g ~ 1/16
n^2.
  For GEOMETRIC (polyhedral) surfaces with n vertices the maximal genus is not
known. The current record is g ~ n log n, due to McMullen, Schulz & Wills
(1983). We present these surfaces with a new construction: We find them in
Schlegel diagrams of ``neighborly cubical 4-polytopes,'' as constructed by
Joswig & Ziegler (2000).

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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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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: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph