We prove that RP 2e −1
نویسندگان
چکیده
This improves, in these cases, by 1 dimension upon the result of Milgram [8], who proved, by constructing bilinear maps, that if n ≡ 7 mod 8, then RPn can be immersed in R2n−α(n)−4 , where α(n) denotes the number of 1s in the binary expansion of n. In [2, Theorem 1.2], the first and fourth authors used obstruction theory to prove that if n ≡ 7 mod 8, then RPn can be immersed in R2n−D , where D = 14, 16, 17, 18 if α(n) = 7, 8, 9,≥ 10. That result, with n = 2e − 1, is stronger than ours for e ≤ 12. If e ≥ 13, then our result improves on the result of [2] by e − 13 dimensions. Thus Equation 1.1 improves on all known results by 1 dimension if e ≥ 14.
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