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- W2762949685 abstract "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." @default.
- W2762949685 created "2017-10-20" @default.
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- W2762949685 date "2017-10-04" @default.
- W2762949685 modified "2023-09-27" @default.
- W2762949685 title "Bridge trisections of knotted surfaces in 4--manifolds" @default.
- W2762949685 hasPublicationYear "2017" @default.
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