Some New Embeddings and Nonimmersions of Real Projective Spaces

Theorem 1.1(1) improves on the previously best known result ([1]) by 1 dimension, while Theorem 1.1(2) improves on the previously best known nonimmersion and nonembedding results ([2]) for P 16n+10 and P 16n+11 by 4 dimensions, and is within 1 of best possible for them. It also implies new nonimmersions for P , P , and P . Theorem 1.2 improves on the previously best known embedding ([11]) of P 8n+4 by 1 dimension. These results can best be appreciated when viewed in a table of known embedding and immersion results for real projective spaces. Such a table may be seen on the internet at [3]. The method of proof is obstruction theory, specifically modified Postnikov towers (MPTs). The reason that Theorem 1.1 had not been noticed before is that the first author used to think that nonimmersions were extremely difficult to prove by MPTs because of the possibility of secondary and higher order indeterminacy. We