Tightness for Smooth and Polyhedral Immersions of the Projective Plane with One Handle
نویسنده
چکیده
The recent discovery that there is a tight polyhedral immersion of the projective plane with one handle, while there is no smooth tight immersion of the same surface, provides a rare example in low dimensions of a significant difference between smooth and polyhedral surfaces. In this paper the author shows that the obstruction to smoothing the polyhedral model is not local in nature, and describes some of the ways in which the proof of the nonexistence of the smooth tight surface does not carry over to the polyhedral case.
منابع مشابه
A Tight Polyhedral Immersion in Three-space of the Real Projective Plane with One Handle
In 1960, Nicolaas Kuiper showed that every surface can be tightly immersed in three-space except for the real projective plane and the Klein bottle, for which no such immersion exists, and the real projective plane with one handle, for which he could find neither a tight example nor a proof that one does not exist. It was not until more than 30 years later, in 1992, that François Haab proved th...
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