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The complex manifold ℂℙ  n   × ℂℙ  n +1  with symplectic formσ   μ    =   σ    CP    n+  μ   σ    CP    n    +  1, whereσ    CP    nandμ   σ    CP    n    +  1are normalized Fubini–Study forms,  n  ∈ ℕ and μ > 1 a real number, contains a natural Lagrangian sphere  L  μ . We prove that the Dehn twist along  L  μ  is symplectically isotopic to the identity for all μ > 1. This isotopy can be chosen so that it pointwise fixes a complex hypersurface in ℂℙ  n   × ℂℙ  n +1  and lifts to the blow‐up of ℂℙ  n   × ℂℙ  n +1  along a complex  n ‐dimensional submanifold.

A symplectic isotopy of a Dehn twist on ℂℙ n × ℂℙ n +1