6 votes
Accepted

Symplectic diffeomorphism of the cylinder moving a point to 0

The symplectic group acts (n)-transitively on connected manifolds of dim $\geq 2$. See Michor and Vizman n-Transitivity of certain diffeomorphism groups https://arxiv.org/pdf/dg-ga/9406005.pdf (1)-...
Thomas Rot's user avatar
  • 7,363
2 votes

What is so geometric about symplectic geometry?

My take on this is fairly simple-minded. A metric is a non-degenerate symmetric bilinear form on a vector space. This yields a notion of distance, angle and volume. Dually, we can define a 'cometric' ...
Mozibur Ullah's user avatar
1 vote

Fredholm property of linearization of Floer map

They show in Section 8.7.c that $(dF^H)_u$ is a Fredholm operator. What remains is simple linear algebra (even continuity is irrelevant). Suppose $A: V \times W \to U$ is a linear map, with $B = A|_V$ ...
mme's user avatar
  • 9,263

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