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

David T. Gay; Robion Kirby

doi:10.1073/pnas.1018465108

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arXiv · 1102.2169

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

David T. Gay·Robion Kirby

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Abstract

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 1-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.

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BibTeX RIS

David T. Gay, Robion Kirby. 2011-02-10. Fiber connected, indefinite Morse 2-functions on connected n-manifolds. https://doi.org/10.1073/pnas.1018465108

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