CSpace
Finiteness and infiniteness results for Torelli groups of (hyper-)Kahler manifolds
Kreck, Matthias1,2; Su, Yang3,4
2021-04-12
Source PublicationMATHEMATISCHE ANNALEN
ISSN0025-5831
Pages12
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].
DOI10.1007/s00208-021-02174-x
Indexed BySCI
Language英语
Funding ProjectProjekt DEAL
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000639368700001
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58440
Collection中国科学院数学与系统科学研究院
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
Recommended Citation
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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Kreck, Matthias]'s Articles
[Su, Yang]'s Articles
Baidu academic
Similar articles in Baidu academic
[Kreck, Matthias]'s Articles
[Su, Yang]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Kreck, Matthias]'s Articles
[Su, Yang]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.