Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a quadratic form associated with a surface automorphism and its
  applications to Singularity Theory   We study the nilpotent part $N'$ of a pseudo-periodic automorphism $h$ of a
real oriented surface with boundary $\Sigma$. We associate a quadratic form $Q$
defined on the first homology group (relative to the boundary) of the surface
$\Sigma$. Using the twist formula and techniques from mapping class group
theory, we prove that the form $\tilde{Q}$ obtained after killing ${\ker N}$ is
positive definite if all the screw numbers associated with certain orbits of
annuli are positive. We also prove that the restriction of $\tilde Q$ to the
absolute homology group of $\Sigma$ is even whenever the quotient of the
Nielsen-Thurston graph under the action of the automorphism is a tree. The case
of monodromy automorphisms of Milnor fibers $\Sigma=F$ of germs of curves on
normal surface singularities is discussed in detail, and the aforementioned
results are specialized to such situation. Moreover, the form $\tilde{Q}$ is
computable in terms of the dual resolution or semistable reduction graph, as
illustrated with several examples. Numerical invariants associated with
$\tilde{Q}$ are able to distinguish plane curve singularities with different
topological types but same spectral pairs. Finally, we discuss a generic linear
germ defined on a superisolated surface. In this case the plumbing graph is not
a tree and the restriction of $\tilde Q$ to the absolute monodromy of
$\Sigma=F$ is not even.

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The categories of this paper are: physics
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The categories of this paper are: econ
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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: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol