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"Hidden torsion, 3-manifolds, and homology cobordism"

Title 
"Hidden torsion, 3-manifolds, and homology cobordism"
Authors 
Cha, JC; Orr, KE; 차재춘
Issue Date 
2013-01
Journal Title 
JOURNAL OF TOPOLOGY
Volume 
6
Issue 
2
Start Page 
490
Last Page 
512
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.
Keywords 
LINK CONCORDANCE GROUP, LOWER CENTRAL SERIES, ALGEBRAIC CLOSURE, KNOT CONCORDANCE, LENS SPACES, INVARIANTS, LOCALIZATION, L-2-SIGNATURES, CYLINDERS, STABILITY
URI 
http://oasis.postech.ac.kr/handle/2014.oak/14899
DOI 
http://dx.doi.org/10.1112/JTOPOL/JTT003
ISSN 
1753-8416
Article Type 
ARTICLE
Citation 
JOURNAL OF TOPOLOGY, v.6, no.2, pp.490-512
Appears in Collections
Mathematics (수학과) > 1. Journal Papers

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