4
votes
1answer
361 views

Is the space of smooth partitions of unity connected? Simply-connected?

One of the requirements for a smooth manifold $M$ is that it be paracompact, and one of the equivalent definitions of paracompactness for a smooth space is that for overy open cover of $M$, there ...
10
votes
0answers
373 views

Exotic smoothness and Parallelizability

Regarding the parallelizability of the Milnor's seven dimensional exotic spheres: Parallelizability of the Milnor's exotic spheres in dimension 7 The following question naturally arises: Suppose ...
54
votes
4answers
2k views

Parallelizability of the Milnor's exotic spheres in dimension 7

Are the Milnor's seven dimensional exotic spheres parallelizable?
7
votes
2answers
1k views

Slice knots and exotic $\mathbb R^4$

In the http://arxiv.org/abs/math/0606464v1 I read "If you want to prove existence of exotic smooth structure on $\mathbb R^4$ you can do this if you are in possession of a knot which is ...