Indefinite Morse 2-functions; broken fibrations and generalizations
Indefinite Morse 2-functions; broken fibrations and generalizations
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不定莫尔斯 2 函数；
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. Kirby
中科院分区：
文献类型：
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作者：
David T. Gay;R. Kirby
莫尔斯2-函数是从光滑流形到曲面的一般光滑映射。在没有确定折叠的情况下（在这种情况下，我们说莫尔斯2-函数是不确定的），这些是断裂（莱夫谢茨）纤维化的自然推广。证明了不定莫尔斯2-函数映射到任意紧定向曲面的存在唯一性结果。“唯一性”意味着有一组移动足以在两个同伦不定莫尔斯2-函数之间移动，而始终保持不定。我们推广的存在性和唯一性的结果，不确定的，莫尔斯2-函数的连接纤维。
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.