Topological properties of Reeb orbits on boundaries of star-shaped domains in R4

Details Topological properties of Reeb orbits on boundaries of star-shaped domains in R4 Topological properties of Reeb orbits on boundaries of star-shaped domains in R4

2009-11-18

arxiv.org/abs/0911.3617v2

Mathematics

Geometric Topology

Theorem 1 strengthened, proof of Theorem 2 corrected. Final version, 23 p, 1 figure

Scientific paper

Let c be a periodic Reeb orbit on the boundary S of a compact star-shaped domain C in R4. We show that if there is an immersed symplectic disc f in C with boundary c then the self-linking number lk(c) of c equals 2 tan(f)-1 where tan(f) is the tangential self-intersection number of f. We also show that if C is convex and if the principal curvatures of S are suitably pointwise pinched then the self-linking number of a periodic Reeb orbit of Maslov index 3 equals -1.

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