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- W1972180978 abstract "REMARK. Since 7rk+p( Vk+m,m)W7k+p( Vk+?+2,p+2) for m _p+2, the periodicity theorem can be sharpened to read 20(P+') if p+2_?m. PROOF. It is known [3] that the (2k-1)-skeleton of Vk+m,m is of the same homotopy type as that of Pk+mi Pk+m-1/Pk-l, where Pn is the real n-dimensional projection space. On the other hand, kt+m-l is the Thom complex of kHmi, (which we will write as T(kHm-1)), where Hmi, is the Hopf bundle over Pm-1. To see this, observe that Pk+m-1 -Pk-1kHm_, from which the statement follows immediately. Now (k+20(m-1))Hmi = kHmiGE32,0(m-l)I, where I is the trivial line bundle over Pm-i [1]. Hence T((k+20(m-l))Hm-1) = 2 (m)T(kHm_i). Now the theorem follows from the suspension theorem." @default.
- W1972180978 created "2016-06-24" @default.
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- W1972180978 date "1965-06-01" @default.
- W1972180978 modified "2023-10-18" @default.
- W1972180978 title "A Short Proof of the James Periodicity of π k+p (V k+m,m )" @default.
- W1972180978 cites W2326898909 @default.
- W1972180978 doi "https://doi.org/10.2307/2034684" @default.
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