Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum

Abstract

A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. In the published version of "Mapping class group and a global Torelli theorem for hyperkahler manifolds" I made an error based on a wrong quotation of Dennis Sullivan's famous paper "Infinitesimal computations in topology". I claimed that the natural homomorphism from the mapping class group to the group of automorphims of cohomology of a simply connected Kahler manifold has finite kernel. In a recent preprint arXiv:1907.05693, Matthias Kreck and Yang Su produced counterexamples to this statement. Here I correct this error and other related errors, observing that the results of "Mapping class group and a global Torelli theorem" remain true after an appropriate change of terminology.

9 pages, version 2.1, small improvements throughout, minor errors squashed

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Cited by in corpus (60)

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• Hyperkähler fourfolds and Kummer surfaces
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• The LLV decomposition of hyper-Kaehler cohomology
• Non-symplectic involutions of irreducible symplectic manifolds of K3^[n]-type
• No cohomologically trivial non-trivial automorphism of generalized Kummer manifolds
• Teichmuller space for hyperkahler and symplectic structures
• Contraction centers in families of hyperkahler manifolds
• On the existence of universal families of marked irreducible holomorphic symplectic manifolds
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• Finiteness of Klein actions and real structures on compact hyperkähler manifolds
• A counterexample to the birational Torelli problem for Calabi-Yau threefolds
• Tautological classes on moduli space of hyperkähler manifolds
• Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational
• A classification of Lagrangian planes in holomorphic symplectic varieties
• Complex ball quotients from manifolds of $K{3}^{[n]}$-type
• On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
• Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry
• Unobstructed symplectic packing for tori and hyperkahler manifolds
• Symplectic birational transformations of finite order on O'Grady's sixfolds
• From local Torelli to global Torelli
• Towards a classification of symplectic automorphisms on manifolds of $K{3}^{[n]}$ type
• Construction of automorphisms of hyperkähler manifolds
• Extremal rays and automorphisms of holomorphic symplectic varieties
• Symplectic involutions of $K{3}^{[n]}$ type and Kummer $n$ type manifolds
• On the Kodaira Dimension of the Moduli of Deformation Generalised Kummer Varieties
• k-symplectic structures and absolutely trianalytic subvarieties in hyperkahler manifolds
• On the period of Lehn, Lehn, Sorger, and van Straten's symplectic eightfold
• On polarization types of Lagrangian fibrations
• Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
• On Irreducible Symplectic Varieties of ${K3}^{[n]}$-type in Positive Characteristic
• Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
• Non-symplectic automorphisms of odd prime order on manifolds of $K{3}^{[n]}$-type
• A local Torelli theorem for log symplectic manifolds
• Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic
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• Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
• Every rational Hodge isometry between two K3 surfaces is algebraic
• Parabolic automorphisms of hyperkahler manifolds
• Supersingular O'Grady varieties of dimension six
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• On the GHKS compactification of the moduli space of K3 surfaces of degree two
• Mapping class group of manifolds which look like $3$-dimensional complete intersections
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• On symplectic birational self-maps of projective hyperkähler manifolds of K3${}^{[n]}$-type
• Towards a modular construction of OG10
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• Non-symplectic involutions on manifolds of $K{3}^{[n]}$-type
• Hyper-Kaehler compactification of the intermediate Jacobian fibration of a cubic fourfold : the twisted case
• Rigidity of Lagrangian embeddings into symplectic tori and K3 surfaces
• On subgroups of an automorphism group of an irreducible symplectic manifold
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• Complex structures, moment maps, and the Ricci form (Extended Version)