Abstract
A Morse 2-function is a generic smooth map f from a manifold M of arbitrary finite dimension to a surface B. Its critical set maps to an immersed collection of cusped arcs in B. The aim of this paper is to explain exactly when it is possible to move these arcs around in B by a homotopy of f and to give a library of examples when M is a closed 4-manifold. The last two sections give applications to the theory of crown diagrams of smooth 4-manifolds.
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Acknowledgements
The author would like to thank Denis Auroux, David Gay and Yankı Lekili for helpful conversations during the preparation of this work.
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Williams, J.D. Existence of two-parameter crossings, with applications. Geom Dedicata 207, 265–286 (2020). https://doi.org/10.1007/s10711-019-00499-1
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DOI: https://doi.org/10.1007/s10711-019-00499-1