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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
8
votes
Theorems that led to very successful research programs in Geometry and Topology
Haynes Miller's resolution of the Sullivan conjecture.
Adams' solution if the Hopf invariant one problem.
2
votes
looking for a book on banach manifolds
I happen to know this
Abraham, Ralph; Robbin, Joel
Transversal mappings and flows.
An appendix by Al Kelley W. A. Benjamin, Inc., New York-Amsterdam 1967 x+161 pp.
exists.
1
vote
"structure group" for fibration
My advisor (Sufian Husseini) wrote a book where something like this is done, based on the work in some of his first papers.
Husseini, S. Y.
The topology of classical groups and related topics. Gordon …
0
votes
A question about the inverse theorem function in $\mathbb{R}^n$
$f(x,y)=(xy,y)$ is a counterexample.