Some new immersion results for complex projective space

 Donald M. Davis 

dmd1@lehigh.edu

Lehigh University, Bethlehem, PA 18015

Abstract:
We prove the following two new optimal immersion results for complex projective space.
First, if n equiv 3 mod 8 but n not equiv 3 mod 64, and alpha(n)=7, then CP^n can be immersed in R^{4n-14}.
Second, if n is even and alpha(n)=3, then CP^n can be immersed in R^{4n-4}.
Here alpha(n) denotes the number of 1's in the binary expansion of n.
The first contradicts a result of Crabb, who said that such an immersion does not exist,
apparently due to an arithmetic mistake.