All Questions
Tagged with differential-topology jets
3 questions
7
votes
1
answer
4k
views
Short and elegant definition of the $C^1$ topology
A friend told me that the $\mathbf{C^1}$-topology on the set $C^\infty(M,N)$ of smooth functions between two smooth manifolds $M$ and $N$ can be defined as the coarsest topology making the map
$$
C^\...
2
votes
2
answers
351
views
Constructing jet bundles from a cocycle of smooth transition functions
Suppose we are given an open cover $\mathcal{U}=(U_{i})_{i \in I}$ of a smooth manifold $M$, a cocycle of smooth transition functions $g_{ij}: U_{ij} \to G$ where $G$ is a Lie group, and a (not ...
1
vote
0
answers
105
views
Codimension of cusp singularities in the space of 2-jets
In trying to prove Cerf's theorem about homotopies between Morse-functions I ended up thinking about the following problem.
For $n>2$, $a= (a_{i,j})\in GL(n-2)$, we define the polynomial map $C_a:\...