Finiteness and infiniteness results for Torelli groups of (hyper-)Kahler manifolds

doi:10.1007/s00208-021-02174-x

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	Finiteness and infiniteness results for Torelli groups of (hyper-)Kahler manifolds
	Kreck, Matthias 1,2; Su, Yang 3,4
	2021-04-12
发表期刊	MATHEMATISCHE ANNALEN
ISSN	0025-5831
页码	12
摘要	The 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].
DOI	10.1007/s00208-021-02174-x
收录类别	SCI
语种	英语
资助项目	Projekt DEAL
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000639368700001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58440
专题	中国科学院数学与系统科学研究院
通讯作者	Kreck, Matthias
作者单位	1.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
推荐引用方式 GB/T 7714	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.