DIFFERENTIAL GEOMETRY/PDE SEMINAR

                            Monday, April 22

                             Padelford C401
                                3:45 PM

                 KOHN-ROSSI COHOMOLOGY OF CR MANIFOLDS

                           Peter M. Garfield
                       (University of Washington)


A CR manifold is an abstract model of a real hypersurface in C^n.  In
another sense, a CR manifold is the generalization of a complex
structure to a real odd-dimensional manifold.  As such, the Kohn-Rossi
cohomology is the analogue of the cohomology generated by the
Cauchy-Riemann complex.  This cohomology is linked to various CR
embedding questions, and is thus of significant interest.

In 1994, M. Rumin reproduced de Rham cohomology on contact manifolds
(including, for example, a certain class of CR manifolds) using a
resolution of the constant sheaf R.  In 1993, T. Akahori and K. Miyajima
produced a finer double complex that corresponded to the second half of
Rumin's complex.  Moreover, Akahori and Miyajima's complex reproduced
Kohn-Rossi cohomology in these upper dimensions.  We produce a
collection of resolutions that generalize Rumin's resolution and
incorporate the complexes of Akahori and Miyajima.  These resolutions
reproduce Kohn-Rossi cohomology.

Finally, we will briefly remark on recent work by S. Yau and H. S. Luk
relating the CR embeddability of certain CR manifolds to their
Kohn-Rossi cohomology.


For more information about this seminar, view the Differential Geometry
Seminar World-Wide Web page at 

    https://www.math.washington.edu/~lee/Seminars/dg.html


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