Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: k-Normal surfaces   Following Matveev, a k-normal surface in a triangulated 3-manifold is a
generalization of both normal and (octagonal) almost normal surfaces. Using
spines, complexity, and Turaev-Viro invariants of 3-manifolds, we prove the
following results: 1) a minimal triangulation of a closed irreducible or a
bounded hyperbolic 3-manifold contains no non-trivial k-normal sphere; 2) every
triangulation of a closed manifold with at least 2 tetrahedra contains some
non-trivial normal surface; 3) every manifold with boundary has only finitely
many triangulations without non-trivial normal surfaces. Here, triangulations
of bounded manifolds are actually ideal triangulations. We also calculate the
number of normal surfaces of nonnegative Euler characteristics which are
contained in the conjecturally minimal triangulations of all lens spaces.

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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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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: funct-an
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The categories of this paper are: quant-ph
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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: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc