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

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

2011-02-10

arxiv.org/abs/1102.2169v2

Mathematics

Geometric Topology

12 pages, 8 figures, to appear in Proc. Nat. Acad. Sci. U.S.A. This contains a condensed presentation of most of the results i

Scientific paper

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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