Classifying space for U(n): Difference between revisions

Revision as of 18:46, 26 April 2009

Revision as of 18:47, 26 April 2009

Line 31:

: <math>\begin{align}

F_n(\mathbb{C}^k) & \longrightarrow & S^{2k-1} \\

(e_1,\ldots,e_n) & \longmapsto & e_n

\end{align}</math>

Line 43:

: <math>\pi_p(F_n(\mathbb{C}^k)) = \pi_p(F_{n-1}(\mathbb{C}^{k-1})) = \cdots = \pi_p(F_1(\mathbb{C}^{k+1-n})) = \pi_p(S^{k-n}).</math>

This last group is trivial for <math>''k''&nbsp;>&nbsp;''n''&nbsp;+&nbsp;''p</math>''. Let

: <math>EU(n)={\lim_{\rightarrow}}\;_{k\rightarrow\infty}F_n(\mathbb{C}^k)</math>