Vertical flows and a general currential homotopy formula

Daniel Cibotaru

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arXiv · 1405.0952

Vertical flows and a general currential homotopy formula

Daniel Cibotaru

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Abstract

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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Daniel Cibotaru. 2014-05-05. Vertical flows and a general currential homotopy formula. https://arxiv.org/abs/1405.0952

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