

Geometric Topology Seminar
June 14, 2012 14:30, Moscow, Steklov Mathematical Institute, room 534






On nonimmersibility of $RP^{10}$ to $R^{15}$
P. M. Akhmet'ev^{}, O. D. Frolkina^{} 
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Abstract:
B. J. Sanderson noted that for $k < n$ the projective space $RP^k$ is immersible in $R^n$ f and only if the tangent bundle $RP^n$ admits $k$ linearly independent vector fields over $RP^k$ [1, Lemma (9.7)]. Using this remark, P. F. Baum and W. Browder proved that $RP^10$ can not be immersed to $R^{15}$ [1, Corollary (9.9)] by showing that the tangent bundle $TRP^{15}$ does not admit $9$ linearly independent vector fields over $RP^{10}$ [1, Thm. (9.5)]. We present a new proof of this last statement based on U. Koschorke
singularity approach [2].
References
[1] P.F. Baum, W.Browder. The cohomology of quotients of classical
groups // Topology 3 (1965), 305–336.
[2] U. Koschorke. Vector Fields and Other Vector Bundle Morphisms —
A Singularity Approach. Lecture Notes in Math. 847 (Springer, Berlin,
1981).

