Geometric structures on contactomorphism groups and contact rigidity in jet spaces

Details Geometric structures on contactomorphism groups and contact rigidity in jet spaces Geometric structures on contactomorphism groups and contact rigidity in jet spaces

2012-02-25

arxiv.org/abs/1202.5691v1

Mathematics

Symplectic Geometry

15 pages

Scientific paper

For a closed connected manifold N, we establish the existence of geometric structures on various subgroups of the contactomorphism group of the standard contact jet space J^1N, as well as on the group of contactomorphisms of the standard contact T*N \times S^1 generated by compactly supported contact vector fields. The geometric structures are biinvariant partial orders (for J^1N and T*N \times S^1) and biinvariant integer-valued metrics (T*N\times S^1 only). Also we prove some forms of contact rigidity in T*N \times S^1, namely that certain (possibly singular) subsets of the form X \times S^1 cannot be disjoined from the zero section by a contact isotopy, and in addition that there are restrictions on the kind of contactomorphisms of T*N\times S^1 which are products of pairwise commuting contactomorphisms generated by vector fields supported in sets of the form U \times S^1 with U \subset T*N Hamiltonian displaceable. The method is that of generating functions for Legendrians in jet spaces.

Affiliated with

Also associated with

No associations

Rating

Geometric structures on contactomorphism groups and contact rigidity in jet spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric structures on contactomorphism groups and contact rigidity in jet spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric structures on contactomorphism groups and contact rigidity in jet spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-291570