Smooth maps between smooth manifolds
Smooth manifolds and smooth maps show up naturally in many fields of mathematics and physics. We study the relationship between properties of a smooth map and those of its source and target manifolds. We present several examples where the topology of the manifolds and the structure of their smooth maps more or less determine each other. Many examples are related to the cobordism theory of singular maps, and we show how to obtain such relations via cobordism invariants of singular maps. We try to find relationships between the smooth structures of manifolds and their singular maps as well.