Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quivers with potentials associated to triangulated surfaces, part IV:
  Removing boundary assumptions   We prove that the quivers with potentials associated to triangulations of
surfaces with marked points, and possibly empty boundary, are non-degenerate,
provided the underlying surface with marked points is not a closed sphere with
exactly 5 punctures. This is done by explicitly defining the QPs that
correspond to tagged triangulations and proving that whenever two tagged
triangulations are related by a flip, their associated QPs are related by the
corresponding QP-mutation. As a byproduct, for (arbitrarily punctured) surfaces
with non-empty boundary we obtain a proof of the non-degeneracy of the
associated QPs which is independent from the one given by the author in the
first paper of the series.
  The main tool used to prove the aforementioned compatibility between flips
and QP-mutations is what we have called \emph{Popping Theorem}, which, roughly
speaking, says that an apparent lack of symmetry in the potentials arising from
ideal triangulations with self-folded triangles can be fixed by a suitable
right-equivalence.

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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: cs