Hidden torsion, 3-manifolds, and homology cobordism

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

2011-01-21

arxiv.org/abs/1101.4092v1

Mathematics

Geometric Topology

23 pages

Scientific paper

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.

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