Enumeration and Normal Forms of Singularities in Cauchy-Riemann
Structures.
Dissertation, University of Chicago, 1997.
Chapter II. Degeneracy Loci in CR Geometry
abstract for Chapter II:
The objects of study are real m-submanifolds M of complex n-manifolds.
The goal is to describe the topological and complex-analytic behavior
of submanifolds with complex tangents--- points where the tangent
space and its rotation by the complex structure operator do not meet
transversely.
Complex tangents of M form a degeneracy locus of a bundle map over M.
When the immersion of M is generic with respect to a transversality
condition on the Gauss map, a construction of Thom and Porteous is
used in a theorem relating the fundamental class of the locus to chern
and pontrjagin classes. Recent theorems of Fulton and Pragacz are
applied to describe other global complex tangency phenomena.
remarks:
The author has made a few minor editorial modifications so that
Chapter II can stand alone. Section 5 of Chapter II is a summary of
results appearing in the unpublished lecture notes ``Invariants for
Pairs of Almost Complex Structures,'' which contains the Figure
omitted here. This (Chapter II) file also displays the dissertation's
comprehensive bibliography.
The main results from the remaining chapters of the dissertation
appear in the unpublished manuscript ``Formal Stability of the CR
Cross-Cap,'' and the unpublished lecture notes, ``Complexification of
the CR Cross-Cap.''