Normal invariants of products (Ex)

Latest revision as of 23:41, 27 August 2013

Let $<wikitex>; Let $(f, b) \colon M \to X$ and $(g, c) \colon N \to Y$ be degree one normal maps of closed smooth manifolds $X$ and $Y$ with normal invariants $\eta_X(f, b) \in [X, G/O]$ and $\eta_Y(g, c) \in [Y, G/O]$. {{beginthm|Exercise}} Determine the normal invariant, $$\eta_{X \times Y}(f \times g, b \times c \colon M \times N \to X \times Y) \in [X \times Y, G/O],$$ in terms of $\eta_X(f, b)$ and $\eta_Y(g, c)$. {{endthm}} </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]](f, \bar f) \colon M \to X$ and $(g, \bar g) \colon N \to Y$ be degree one normal maps of closed smooth manifolds $X$ and $Y$ with normal invariants $\eta_X(f, \bar f) \in [X, G/O]$ and $\eta_Y(g, \bar g) \in [Y, G/O]$.

Exercise 0.1.

Determine the normal invariant,

$$\displaystyle \eta_{X \times Y}(f \times g, \bar f \times \bar g \colon M \times N \to X \times Y) \in [X \times Y, G/O],$$

in terms of $\eta_X(f, \bar f)$ and $\eta_Y(g, \bar g)$.

References