Hidden torsion, 3-manifolds, and homology cobordism
SCIE
SCOPUS
- Title
- Hidden torsion, 3-manifolds, and homology cobordism
- Authors
- Cha, JC; Orr, KE
- Date Issued
- 2013-01
- Publisher
- OXFORD UNIV PRESS
- Abstract
- This paper continues our exploration of homology cobordism of 3-manifolds using our recent results on Cheeger-Gromov rho-invariants associated to amenable representations. We introduce a new type of torsion in 3-manifold groups that we call hidden torsion, and an algebraic approximation we call local hidden torsion. We construct infinitely many hyperbolic 3-manifolds which have local hidden torsion in the transfinite lower central subgroup. By realizing Cheeger-Gromov invariants over amenable groups, we show that our hyperbolic 3-manifolds are not pairwise homology cobordant, yet remain indistinguishable by any prior known homology cobordism invariants. Additionally, we give an answer to a question about transfinite lower central series of homology cobordant 3-manifold groups, asked by T. D. Cochran and M. H. Freedman.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/14899
- DOI
- 10.1112/JTOPOL/JTT003
- ISSN
- 1753-8416
- Article Type
- Article
- Citation
- JOURNAL OF TOPOLOGY, vol. 6, no. 2, page. 490 - 512, 2013-01
- Files in This Item:
- There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.