I will describe a new constraint on the topology of Lefschetz fibrations with 4-dimensional fibers, arising from the analysis of the framed bordism class of Seiberg–Witten moduli spaces. This constraint yields smooth isotopy obstructions for compositions of Dehn twists along self-intersection -2 spheres in 4-manifolds. As an application, we give a negative answer to a question of Donaldson asking whether, for a closed simply-connected symplectic 4-manifold, the symplectic Torelli group is generated by squared Dehn twists on Lagrangian spheres.

Based on joint work with H. Konno, J. Lin, and A. Mukherjee.