Degrees of maps in algebraic topology Please can I have some tips on how to construct maps between topological spaces of a given degree? For example, how would you go about building a map of degree $3$ from $\mathbb{CP}^1\times\mathbb{CP}^2 \to \mathbb{CP}^3$? Or a map from $S^2\times S^2 \to \mathbb{CP}^2$ of even degree? I don't know where to start. Are there any particular techniques that are useful?

For maps involving projective spaces, an elementary technique is to try to find a surjection involving homogeneous polynomials-you have coordinates in this case, so you should use them.  Given polynomial maps $p:\mathbb{C} P^1\to \mathbb{C} P^3$ and $q:\mathbb{C} P^2\to \mathbb{C} P^3$ I can construct $pq$ by multiplying coordinatewise: adding wouldn't preserve well-definedness, but multiplying does, as in $([z:w],[a:b:c])\mapsto [za^2:wb^2:zc^2:w(a^2+2b^2+3c^2)].$  A similar technique might do the $S^2\times S^2\to \mathbb{C} P^2$ case, since that's also a map out of a product of projective spaces. 
