Journal of Symplectic Geometry

Volume 12 (2014)

Number 2

Open books for Boothby-Wang bundles, fibered Dehn twists and the mean Euler characteristic

Pages: 379 – 426

DOI: http://dx.doi.org/10.4310/JSG.2014.v12.n2.a6

Authors

River Chiang (Department of Mathematics, National Cheng Kung University, Tainan, Taiwan)

Fan Ding (School of Mathematical Sciences and LMAM, Peking University, Beijing, China)

Otto van Koert (Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, South Korea)

Abstract

We examine open books with powers of fibered Dehn twists as monodromy. The resulting contact manifolds can be thought of as Boothby-Wang orbibundles over symplectic orbifolds. Using the mean Euler characteristic of equivariant symplectic homology we can distinguish these contact manifolds and hence show that some fibered Dehn twists are not symplectically isotopic to the identity relative to the boundary. This complements results of Biran and Giroux.

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