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The incipient infinite cluster in high-dimensional percolation
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## The Nash conjecture for threefolds

### J\'anos Koll\'ar

**Abstract.**
Nash conjectured in 1952 that every compact
differentiable manifold can be realized as the set of real
points of a real algebraic variety which is birational
to projective space. This paper announces the negative
solution of this conjecture in dimension 3.
The proof shows that in fact very few 3-manifolds
can be realized this way.

*Copyright 1998 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**04** (1998), pp. 63-73
- Publisher Identifier: S 1079-6762(98)00049-3
- 1991
*Mathematics Subject Classification*. Primary 14P25
*Key words and phrases*.
- Received by the editors July 17, 1998
- Posted on September 15, 1998
- Communicated by Robert Lazarsfeld
- Comments (When Available)

**J\'anos Koll\'ar**

University of Utah, Salt Lake City, UT 84112

*E-mail address:* `kollar@math.utah.edu`

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