Finiteness and infiniteness results for Torelli groups of (hyper-)Kahler manifolds
Kreck, Matthias1,2; Su, Yang3,4
AbstractThe Torelli group T ( X) of a closed smoothmanifold X is the subgroup of themapping class group pi(0)(Diff(+) ( X)) consisting of elements which act trivially on the integral cohomology of X. In this note we give counterexamples to Theorem 3.4 by Verbitsky (DukeMath J 162(15):2929-2986, 2013) which states that the Torelli group of simply connected Kahler manifolds of complex dimension >= 3 is finite. This is done by constructing under some mild conditions homomorphisms J : T (X) -> H-3(X; Q) and showing that for certain Kahler manifolds this map is non-trivial. We also give a counterexample to Theorem 3.5 (iv) in (Verbitsky in Duke Math J 162(15):2929-2986, 2013) where Verbitsky claims that the Torelli group of hyperkahler manifolds are finite. These examples are detected by the action of diffeomorphsims on pi(4)( X). Finally we confirm the finiteness result for the special case of the hyperkahler manifold K-[2].
Indexed BySCI
Funding ProjectProjekt DEAL
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000639368700001
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Document Type期刊论文
Corresponding AuthorKreck, Matthias
Affiliation1.Univ Bonn, Math Inst, Bonn, Germany
2.Goethe Univ Frankfurt, Math Inst, Frankfurt, Germany
3.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
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Kreck, Matthias,Su, Yang. Finiteness and infiniteness results for Torelli groups of (hyper-)Kahler manifolds[J]. MATHEMATISCHE ANNALEN,2021:12.
APA Kreck, Matthias,&Su, Yang.(2021).Finiteness and infiniteness results for Torelli groups of (hyper-)Kahler manifolds.MATHEMATISCHE ANNALEN,12.
MLA Kreck, Matthias,et al."Finiteness and infiniteness results for Torelli groups of (hyper-)Kahler manifolds".MATHEMATISCHE ANNALEN (2021):12.
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