A BORSUK-ULAM TYPE THEOREM OVER ITERATED SUSPENSIONS OF REAL PROJECTIVE SPACES

Title & Authors
A BORSUK-ULAM TYPE THEOREM OVER ITERATED SUSPENSIONS OF REAL PROJECTIVE SPACES
Tanaka, Ryuichi;

Abstract
A CW complex B is said to be I-trivial if there does not exist a $\small{\mathbb{Z}_2}$-map from $\small{S^{i-1}}$ to S($\small{{\alpha}}$) for any vector bundle $\small{{\alpha}}$ over B a any integer i with i > dim $\small{{\alpha}}$. In this paper, we consider the question of determining whether $\small{\Sigma^k\mathbb{R}P^n}$ is I-trivial or not, and to this question we give complete answers when k $\small{\neq}$ 1, 3, 8 and partial answers when k
Keywords
sphere bundle;$\small{\mathbb{Z}_2}$-map;index;
Language
English
Cited by
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