Hidden torsion, 3-manifolds, and homology cobordism
| Autor: | Cha, Jae Choon, Orr, Kent E. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/jtopol/jtt003 |
| Popis: | 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. Comment: 24 pages; a new theorem answering a question of Cochran and Freedman (Kirby List 3.78) added; referee's comments incorporated; to appear in J. Topology |
| Databáze: | arXiv |
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