Riccardo Pedrotti | Searcharxiv

arXiv2026

On sections of Lefschetz fibrations and bundles over 2-complexes

We address the question of existence of sections of fibrations in two settings. First, we show that a bundle with base a finite 2-complex admits a section if and only if the inclusion of the fiber is $\pi_1$-injective and the associated short exact sequence of fundamental groups splits. Second, for Lefschetz fibrations over the disk we provide a complete algebraic criterion characterizing which loops in the boundary mapping torus extend to continuous or smooth sections over the disk. Finally, we apply our results to achiral Lefschetz fibrations over the sphere obtained by doubling along the vertical boundary, and give a criterion ensuring the existence of at least two homologically distinct sections.

math.GT↗

arXiv2023

Fixed point Floer cohomology of disjoint Dehn twists on a w+-monotone manifold with rational symplectic form

We give an explicit description of the Floer cohomology of a family of Dehn twists about disjoint Lagrangian spheres in a w+ - monotone rational symplectic manifold. As a byproduct of our framework, in a monotone symplectic manifold we are able to define a class in the fixed point Floer cohomology of a Dehn twist by counting half strips bound to the given Lagrangian sphere and prove it must vanish. In subsequent work we plan on using this vanishing result to give a new geometric proof of Seidel's long exact sequence.

math.SG↗