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

TL;DR

This paper corrects an earlier error regarding the mapping class group of hyperkähler manifolds, clarifying the relationship with cohomology automorphisms and confirming the validity of previous results after adjustments.

Contribution

It rectifies a mistake in the previous work about the kernel of the homomorphism from the mapping class group to cohomology automorphisms, ensuring the results remain valid with proper terminology.

Findings

Corrected the claim about the kernel being finite.

Confirmed the main results hold after terminology adjustments.

Clarified the relationship between mapping class groups and cohomology automorphisms.

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.