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Contact manifolds, contact structures, contact forms, Reeb dynamics, Legendrian knots, contact homology, symplectic field theory

11 votes

Physical intuition behind prequantization spaces

If you think instead of the prequantum line bundle (i.e. the complex line bundle associated to your prequantum circle bundle using the standard representation of the circle on $\mathbb{C}$) then the s …
Jonny Evans's user avatar
  • 7,005
5 votes

Symplectic Submanifolds of Contact Manifolds and Contact Submanifolds of Symplectic Manifolds

As Chris Gerig indicates in his comment, the correct notion is that of a contact-type hypersurface. These always exist, even locally. You could just take the boundary of a Darboux ball, which always e …
Jonny Evans's user avatar
  • 7,005
3 votes

Contactomorphisms have in general no fixed points

Here's a complement to Dmitri's excellent answer. While it's true that contactomorphisms can have fixed points, even for some open set of contactomorphisms, there is a reason you don't expect to be ab …
Jonny Evans's user avatar
  • 7,005