Fiber-connected, indefinite Morse 2-functions on connected n-manifolds.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 21518894.
- Also identified by DOI 10.1073/pnas.1018465108 and PMC identifier 3100985.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
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.