Related Results:

Since most surfaces have tight immersions, Kuiper asked whether, for a given surface, tight immersions can be found in each class of immersion under regular homotopy. In 1985, Pinkall [P1] showed that such immersions can be found for all but finitely many of these classes. He exhibits polyhedral models of several important classes, and shows that they can be smoothed to obtain examples for both the smooth and polyhedral cases.

Unfortunately, there is an error in one of his examples, which leaves an infinite class of immersions with no known examples. In 1993, Cervone [to appear] located and corrected this error in Pinkall's work, and succeeded in producing polyhedral models of several of the classes of immersions for which no tight example was previously known, leaving the situation for only two classes yet to be resolved.

The bibliography also includes references to papers with related results, in particular, to higher-dimensional analogues.

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8/13/94 dpvc@geom.umn.edu -- The Geometry Center