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Fiber-connected, indefinite Morse 2-functions on connected n-manifolds

By David T. Gay and Robion C. Kirby


We discuss generic smooth maps from smooth manifolds to smooth surfaces, which we call “Morse 2-functions,” and homotopies between such maps. The two central issues are to keep the fibers connected, in which case the Morse 2-function is “fiber-connected,” and to avoid local extrema over one-dimensional submanifolds of the range, in which case the Morse 2-function is “indefinite.” This is foundational work for the long-range goal of defining smooth invariants from Morse 2-functions using tools analogous to classical Morse homology and Cerf theory

Topics: Low Dimensional Geometry and Topology Special Feature
Publisher: National Academy of Sciences
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Provided by: PubMed Central
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