Indefinite Morse 2-functions; broken fibrations and generalizations
Abstract
A Morse 2-function is a generic smooth map from a smooth manifold to a surface. In the absence of definite folds (in which case we say that the Morse 2-function is indefinite), these are natural generalizations of broken (Lefschetz) fibrations. We prove existence and uniqueness results for indefinite Morse 2-functions mapping to arbitrary compact, oriented surfaces. "Uniqueness" means there is a set of moves which are sufficient to go between two homotopic indefinite Morse 2-functions while remaining indefinite throughout. We extend the existence and uniqueness results to indefinite, Morse 2-functions with connected fibers.
Cite
@article{arxiv.1102.0750,
title = {Indefinite Morse 2-functions; broken fibrations and generalizations},
author = {David T. Gay and Robion Kirby},
journal= {arXiv preprint arXiv:1102.0750},
year = {2016}
}
Comments
74 pages, 41 figures; further errors corrected, some exposition added, other exposition improved, following referee's comments