垂直流和一般的流同伦公式
Vertical flows and a general currential homotopy formula
摘要：
推广了Harvey，Lawson和Latschev关于超越公式的一些结果.这里的重点是通过垂直向量场，特别是Morse-Bott-Smale向量场的流动形式。我们证明了一个非常一般的海侵公式，包括也覆盖非紧的情况下的版本。在应用中，我们完整地回答了Quillen的一个问题，构造了Maslov火花，给出了一个精化的Chern-Gauss-Bonnet定理的简短证明，并重新证明了Nicolaescu和Getzler的一些定理。对奇Chern-Weil理论也作了讨论。
英文摘要：
We generalize some of the results of Harvey, Lawson and Latschev about transgression formulas. The focus here is on flowing forms via vertical vector fields, especially Morse-Bott-Smale vector fields. We prove a very general transgression formula including also a version covering non-compact situations. Among applications, we completely answer a question of Quillen, construct the Maslov spark, give a very short proof of a refined Chern- Gauss-Bonnet theorem, and reprove some theorems of Nicolaescu and Getzler. A discussion about odd Chern-Weil theory is also included.
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