title: Fiber-connected, indefinite Morse 2-functions on connected n-manifolds.
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 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.
authors.affiliation: Euclid Lab, Iowa City, IA 52245, USA. d.gay@euclidlab.org.
authors.forename: David T
authors.initials: DT
authors.lastname: Gay
authors.forename: Robion C
authors.initials: RC
authors.lastname: Kirby