Amorós, JaumeMuñoz, VicentePresas, Francisco2023-06-202023-06-2020041527-5256https://hdl.handle.net/20.500.14352/50618We prove that the vanishing spheres of the Lefschetz pen- cils constructed by Donaldson on symplectic manifolds of any dimension are conjugated under the action of the symplec- tomorphism group of the fiber. More precisely, a number of generalized Dehn twists may be used to conjugate those spheres. This implies the non-existence of homologically triv-ial vanishing spheres in these pencils. To develop the proof,we discuss some basic topological properties of the space of asymptotically holomorphic transverse sections.engjournal articlehttp://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.jsg/1118755326http://projecteuclid.orghttp://arxiv.orgrestricted access514SymplecticLefschetz pencilAsymptotically holomorphicGeometría1204 Geometría