# Normal maps - (non)-examples (Ex)

From Manifold Atlas

1a) Give an example of a degree one map of closed -manifolds which cannot be covered by a map of normal bundles.

1b) Give an example of a degree one map of closed -manifolds which cannot be covered by a map of bundles, for any stable bundle .

2) For every integer , give an example of a degree map of closed -manifolds which can be covered by a map of normal bundles.

3) Let denote the oriented surface of genus . Determine the values of for which there is a degree one normal map .