  We discuss an Abel-Jacobi invariant for algebraic cobordism cycles whose
image in topological cobordism vanishes. The existence of this invariant
follows by abstract arguments from the construction of Hodge filtered
cohomology theories in joint work of Michael J. Hopkins and the author. In this
paper, we give a concrete description of the new Abel-Jacobi map and Hodge
filtered cohomology groups for projective smooth complex varieties.
