Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bridge trisections of knotted surfaces in 4--manifolds   We prove that every smoothly embedded surface in a 4--manifold can be
isotoped to be in bridge position with respect to a given trisection of the
ambient 4--manifold; that is, after isotopy, the surface meets components of
the trisection in trivial disks or arcs. Such a decomposition, which we call a
\emph{generalized bridge trisection}, extends the authors' definition of bridge
trisections for surfaces in $S^4$. Using this new construction, we give
diagrammatic representations called \emph{shadow diagrams} for knotted surfaces
in 4--manifolds. We also provide a low-complexity classification for these
structures and describe several examples, including the important case of
complex curves inside $\mathbb{CP}^2$. Using these examples, we prove that
there exist exotic 4--manifolds with $(g,0)$--trisections for certain values of
$g$. We conclude by sketching a conjectural uniqueness result that would
provide a complete diagrammatic calculus for studying knotted surfaces through
their shadow diagrams.

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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: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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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: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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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: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org