Transfer maps in calculus, algebra, and topology



Abstract: Transfer maps (also known as "umkehr" or wrong-way maps) are certain sorts of functions that go in an unexpected direction. In other words, their source and target are opposite from what is expected in the given context. Transfer maps can provide surprisingly deep information about the objects that they are defined on. I will show you some examples that you may already know very well, and then will describe a more exotic transfer map that arises by understanding the geometry of loops in an algebraic way.