Knot concordance and von Neumann \(\rho\)-invariants

DOI10.1215/S0012-7094-07-13723-2zbMath1186.57006arXivmath/0411057MaRDI QIDQ879624

Peter Teichner, Tim D. Cochran

Publication date: 14 May 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411057

zbMATH Keywords

concordancevon Neumann algebraknotAlexander module\(\rho\)-invariantBlanchfield pairinggropenon-commutative localizationWhitney filtration

Mathematics Subject Classification ID

Topology of infinite-dimensional manifolds (57N20)

Related Items

Noncommutative knot theory ⋮ Symmetric chain complexes, twisted Blanchfield pairings and knot concordance ⋮ Casson towers and slice links ⋮ Amenable signatures, algebraic solutions and filtrations of the knot concordance group ⋮ Slice knots and knot concordance ⋮ A second order algebraic knot concordance group ⋮ Von Neumann rho invariants and torsion in the topological knot concordance group ⋮ Whitney tower concordance of classical links ⋮ Primary decomposition and the fractal nature of knot concordance ⋮ Topologically slice knots with nontrivial Alexander polynomial ⋮ Infection by string links and new structure in the knot concordance group ⋮ Primary decomposition of knot concordance and von Neumann rho-invariants ⋮ Covering link calculus and iterated Bing doubles ⋮ Unknotted gropes, Whitney towers, and doubly slicing knots ⋮ Homology and derived series of groups. II: Dwyer's theorem. ⋮ Homology cobordism invariants and the Cochran-Orr-Teichner filtration of the link concordance group ⋮ Concordance of links with identical Alexander invariants ⋮ Symmetric Whitney tower cobordism for bordered 3-manifolds and links ⋮ Derivatives of knots and second-order signatures ⋮ Link concordance, homology cobordism, and Hirzebruch-type defects from iterated \(p\)-covers ⋮ Higher-order Alexander invariants and filtrations of the knot concordance group ⋮ The first-order genus of a knot ⋮ Satellites of infinite rank in the smooth concordance group ⋮ The bipolar filtration of topologically slice knots ⋮ Knot concordance and higher-order Blanchfield duality ⋮ Link concordance and generalized doubling operators ⋮ A Topological Approach to Cheeger-Gromov Universal Bounds for von Neumann ρ-Invariants ⋮ Linear independence of cables in the knot concordance group ⋮ Splittings of von Neumann rho-invariants of knots ⋮ Correction to the article ``An infinite-rank summand of topologically slice knots ⋮ Up to topological concordance, links are strongly quasipositive ⋮ Primary decomposition in the smooth concordance group of topologically slice knots ⋮ Two-torsion in the grope and solvable filtrations of knots ⋮ Whitney towers, gropes and Casson-Gordon style invariants of links ⋮ New topologically slice knots ⋮ Homology and derived series of groups.

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