Homotopy characteristic classes of foliations
Steven Hurder, Daniel J. Lehmann · Illinois Journal of Mathematics · 1990
The main point of this paper is to use minimal model theory to define new, higher order cohomology invariants of concordance classes of foliations, and then to apply these to establish the existence of uncountable families of distinct foliations on a much wider class of manifolds than previously had been shown.In some sense, this work can be considered as a sequel to the earlier paper [H2] of the first author.Letbe a smooth (i.e., C) foliation on a manifold V without boundary.Let f-: WOq fDn(V) denote the characteristic homomorphism of -(e.g., see [B] or [KT]), where we define the differential graded commutative R-algebra (dgca) Wq A(hl, h2,... hq) (R) R[Cl, c2,... Cq]/(deg > 2q) (deg h 2i 1, deg c 2i, dh ci) and WOq denotes the subalgebra WOq A(h1, h3,..., ha, ) (R) R[c,, c2,...,ca]/(deg > 2q) with q' the largest odd integer DR(V), which induces a map in cohomology f-,s depending only on the concordance class ofand the homotopy class [s] of s.Notethat the map f-, will, in general, vary with the choice of[s] (which was a key point in the paper [H3]).