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"Hidden torsion, 3-manifolds, and homology cobordism"
- "Hidden torsion, 3-manifolds, and homology cobordism"
- Issue Date
- Journal Title
- JOURNAL OF TOPOLOGY
- Start Page
- Last Page
- OXFORD UNIV PRESS
- 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.
- LINK CONCORDANCE GROUP, LOWER CENTRAL SERIES, ALGEBRAIC CLOSURE, KNOT CONCORDANCE, LENS SPACES, INVARIANTS, LOCALIZATION, L-2-SIGNATURES, CYLINDERS, STABILITY
- Article Type
- JOURNAL OF TOPOLOGY, v.6, no.2, pp.490-512
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