Mathematical Research Letters

Volume 10, Issue 1, January 2003 pp. 133-144.

Maximal tori in the contactomorphism groups of circle bundles over Hirzebruch surfaces

Authors: Eugene Lerman
Author institution: University of Illinois, Urbana

Summary: In a recent preprint Yael Karshon showed that there exist non-\linebreak conjugate tori in a group of symplectomorphisms of a Hirzebruch surface. She counted them in terms of the cohomology class of the symplectic structure. We show that a similar phenomenon exists in the contactomorphism groups of pre-quantum circle bundles over Hirzebruch surfaces. Note that the contact structures in question are fillable. This may be contrasted with an earlier paper where we showed that there are infinitely many non-conjugate tori in the contactomorphism groups of certain overtwisted lens spaces ({\it Contact cuts,} Israel J. Math. {\bf 124} (2001), 77--92).

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