Hidden torsion, 3-manifolds, and homology cobordism

Jae Choon Cha; Kent E. Orr

doi:10.1112/jtopol/jtt003

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arXiv · 1101.4092

Hidden torsion, 3-manifolds, and homology cobordism

Jae Choon Cha·Kent E. Orr

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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 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.

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BibTeX RIS

Jae Choon Cha, Kent E. Orr. 2012-12-11. Hidden torsion, 3-manifolds, and homology cobordism. https://doi.org/10.1112/jtopol%2Fjtt003

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