article

Title: Vertical flows and a general currential homotopy formula

Authors: Daniel F Cibotaru

Issue: Volume 65 (2016), Issue 1, 93-169

Abstract:

$We generalize some results of Harvey, Lawson, and Latschev about transgression formulas. The focus here is on flowing forms via vertical vector fields, especially tame Morse-Bott-Smale vector fields. We prove a general transgression formula including also a version covering non-compact situations. A second, companion paper [D. Cibotaru, \textit{Vertical Morse-Bott-Smale flows and characteristic forms}, submitted] contains several applications, one of which is an answer to a question of Quillen. We also prove a Poincar\'e duality result concerning the trangression classes induced by the Pfaffian, construct the Maslov spark, give a short proof of the Chern-Gauss-Bonnet theorem, and re-prove a result of Getzler.$