Invariants for pairs of almost complex structures

Adam Coffman

unpublished lecture notes

For a smooth real linear bundle map between vector bundles equipped
with complex structure operators, the set of points in the base space
where the map respects the complex structures on some subspace is
considered as a degeneracy locus.  A general cohomological formula
describing the generic behavior of the locus is given, with several
examples, including previously known special cases.  The relationships
of this phenomenon with complex tangency of real subbundles, and with
quaternionic structures, are considered.