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A CERTAIN PROPERTY OF POLYNOMIALS AND THE CI-STABILITY OF TANGENT BUNDLE OVER PROJECTIVE SPACES

  • Tanaka, Ryuichi (Department of Liberal Arts Faculty of Science and Technology Tokyo University of Science Noda)
  • Published : 2007.02.28

Abstract

We determine the largest integer i such that $0 and the coefficient of $t^{i}$ is odd in the polynomial $(1+t+t^{2}+{\cdots}+t^{n})^{n+1}$. We apply this to prove that the co-index of the tangent bundle over $FP^{n}$ is stable if $2^{r}{\leq}n<2^{r}+\frac{1}{3}(2^{r}-2)$ for some integer r.

Keywords

sphere bundle;$\mathbb{Z}_2-map$;co-index

References

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