On the mean Euler characteristic of contact manifolds

Details On the mean Euler characteristic of contact manifolds On the mean Euler characteristic of contact manifolds

2010-11-19

arxiv.org/abs/1011.4364v2

Mathematics

Symplectic Geometry

30 pages

Scientific paper

We express the mean Euler characteristic of a contact structure in terms of the mean indices of closed Reeb orbits for a broad class of contact manifolds, the so-called asymptotically finite contact manifolds. We show that this class is closed under subcritical surgery and examine the behavior of the mean Euler characteristic under such surgery. To this end, we revisit the notion of index-positivity for contact forms. We also obtain an expression for the mean Euler characteristic in the Morse-Bott case.

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