Symplectic Mapping Class Group Relations Generalizing the Chain Relation

Abstract

In this paper, we examine mapping class group relations of some symplectic manifolds. For each $n\ge 1$ and $k\ge 1$, we show that the $2n$-dimensional Weinstein domain $W=\{f=\delta \}\cap B^{2n+2}$, determined by the degree $k$ homogeneous polynomial $f\in \mathbb{C}[z_0,\dots ,z_n]$, has a Boothby-Wang type boundary and a right-handed fibered Dehn twist along the boundary that is symplectically isotopic to a product of right-handed Dehn twists along Lagrangian spheres. We also present explicit descriptions of the symplectomorphisms in the case $n=2$ recovering the classical chain relation for the torus with two boundary components.

21 pages, 8 figures; v.4 incorporates several improvements and corrections suggested by the referee; to appear in Internat. J. Math

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Non-fillable invariant contact structures on principal circle bundles and left-handed twists
• On Transverse Knots and Branched Covers

Cited by in corpus (2)

• Lefschetz-Bott fibrations on line bundles over symplectic manifolds
• A four-dimensional mapping class group relation