7

Part of 2016 Miklós Schweitzer

Problems(1)

Unit sphere bundle equivalent to CP^{r-1}

Source: Miklós Schweitzer 2016, Problem 7

Show that the unit sphere bundle of the

r

-fold direct sum of the tautological (universal) complex line bundle over the space

\mathbb{C}P^{\infty}

is homotopically equivalent to

\mathbb{C}P^{r-1}