2012/02/25 by Frol Zapolsky, Zapolsky, Frol
Mathematics · #53D35 #53D99 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D35 #msc:53D99
paper · pdf · doi:10.48550/arxiv.1202.5691
15 pages
arxiv created 2012/02/25 · arxiv updated 2012/02/28
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 J1N, as well as on the group of contactomorphisms of the standard contact T*N × S1 generated by compactly supported contact vector fields. The geometric structures are biinvariant partial orders (for J1N and T*N × S1) and biinvariant integer-valued metrics (T*N× S1 only). Also we prove some forms of contact rigidity in T*N × S1, namely that certain (possibly singular) subsets of the form X × S1 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× S1 which are products of pairwise commuting contactomorphisms generated by vector fields supported in sets of the form U × S1 with U ⊂ T*N Hamiltonian displaceable. The method is that of generating functions for Legendrians in jet spaces.