#diffeomorphisms

In dimensions ≥5, topology and algebra match up simply. In dimensions 3 and 4, manifolds are more interesting. We used to wonder if there was some key idea from high-dimensional manifolds that would extend at least down to dimension 4, making 4-manifolds easy to understand. There is such a principle: Imbedding 2-handles in smooth 4-dimensional manifolds-with-boundary subject to a homotopy criterion.  This high-dimensional idea does work in 4 dimensions and give us insight into 4-manifolds.

diffeomorphisms said: So pretty!!! <3