Exotic iterated Dehn twists

Abstract

Consider cotangent bundles of exotic spheres, with their canonical symplectic structure. They admit automorphisms which preserve the part at infinity of one fibre, and which are analogous to the square of a Dehn twist. Pursuing that analogy, we show that they have infinite order up to isotopy (inside the group of all automorphisms with the same behaviour).

v2: minor changes; v3: temporarily withdrawn; v4: total rewrite; v5: some changes to the topological arguments; v6/7: minor changes, typo removal

References in corpus (4)

• A family of embedding spaces
• Liouville hypersurfaces and connect sum cobordisms
• The Picard-Lefschetz theory of complexified Morse functions
• Symplectic monodromy, Leray residues and quasi-homogeneous polynomials

Cited by in corpus (4)

• Dehn twists exact sequences through Lagrangian cobordism
• The diffeomorphism type of symplectic fillings
• Exotic symplectomorphisms and contact circle actions
• Model projective twists and generalised lantern relations