October 3, 2006
Peter Albers (NYU): Orderability of the universal cover of the group of contactomorphisms of RP3 -- yet another proof
Abstract:
In their paper [EP00] Eliashberg and Polterovich prove that the
universal cover of the (identity component) of the group of
contactomorphisms admits a partial order if and only if there are no
contractible loops of contactomorphisms which are generated by strictly positive time-periodic contact Hamiltonians. As noted by Eliashberg and Polterovich, Givental's non-linear Maslov index yields that RP2n+1 is indeed orderable. A second proof of the orderability of RP3 is due to Eliashberg, Kim and Polterovich via contact homology and relies on the fact RP3 admits a special Weinstein filling, namely T*S2. This works only in dimension 3.
In joint work with Urs Frauenfelder we give a third proof of the orderability of RP3 by proving that a certain Lagrangian torus in T*S2 is not displaceable. This approach was suggested by Polterovich.
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