Some new immersion results for complex projective space

2006/02/21 by Donald M. Davis, Davis, Donald M.
Mathematics · #55S35 #57R42 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.math/0602472

openalex publication_date 2006/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 CPⁿ can be immersed in R^4n-14. Second, if n is even and alpha(n)=3, then CPⁿ 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.

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