scholarly journals Primary decomposition of knot concordance and von Neumann rho-invariants

2020 ◽  
Vol 149 (1) ◽  
pp. 439-447
Author(s):  
Min Hoon Kim ◽  
Se-Goo Kim ◽  
Taehee Kim
Keyword(s):  
Primary Decomposition ◽  
Von Neumann ◽  
Knot Concordance

scholarly journals Knots having the same Seifert form and primary decomposition of knot concordance

2017 ◽  
Vol 26 (14) ◽  
pp. 1750103
Author(s):  
Taehee Kim
Keyword(s):  
Infinite Family ◽  
Alexander Polynomial ◽  
Primary Decomposition ◽  
Amenable Groups ◽  
Von Neumann ◽  
Knot Concordance ◽  
Linearly Independent

We show that for each Seifert form of an algebraically slice knot with nontrivial Alexander polynomial, there exists an infinite family of knots having the Seifert form such that the knots are linearly independent in the knot concordance group and not concordant to any knot with coprime Alexander polynomial. Key ingredients for the proof are Cheeger–Gromov–von Neumann [Formula: see text]-invariants for amenable groups developed by Cha–Orr and polynomial splittings of metabelian [Formula: see text]-invariants.

scholarly journals Knot concordance and von Neumann $\rho$ -invariants

2007 ◽  
Vol 137 (2) ◽  
pp. 337-379 ◽  
Author(s):  
Tim D. Cochran ◽  
Peter Teichner
Keyword(s):  
Von Neumann ◽  
Knot Concordance

Two-torsion in the grope and solvable filtrations of knots

2017 ◽  
Vol 28 (04) ◽  
pp. 1750023 ◽  
Author(s):  
Hye Jin Jang
Keyword(s):  
Primary Decomposition ◽  
Knot Concordance ◽  
Torsion Part

We study knots of order [Formula: see text] in the grope filtration [Formula: see text] and the solvable filtration [Formula: see text] of the knot concordance group. We show that, for any integer [Formula: see text], there are knots generating a [Formula: see text] subgroup of [Formula: see text]. Considering the solvable filtration, our knots generate a [Formula: see text] subgroup of [Formula: see text] [Formula: see text] distinct from the subgroup generated by the previously known [Formula: see text]-torsion knots of Cochran, Harvey, and Leidy. We also present a result on the [Formula: see text]-torsion part in the Cochran, Harvey, and Leidy’s primary decomposition of the solvable filtration.

scholarly journals Primary decomposition in the smooth concordance group of topologically slice knots

2021 ◽  
Vol 9 ◽  
Author(s):  
Jae Choon Cha
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Primary Decomposition ◽  
Direct Sum ◽  
Infinite Rank ◽  
Knot Concordance ◽  
Large Subgroup ◽  
Heegaard Floer

Abstract We address primary decomposition conjectures for knot concordance groups, which predict direct sum decompositions into primary parts. We show that the smooth concordance group of topologically slice knots has a large subgroup for which the conjectures are true and there are infinitely many primary parts, each of which has infinite rank. This supports the conjectures for topologically slice knots. We also prove analogues for the associated graded groups of the bipolar filtration of topologically slice knots. Among ingredients of the proof, we use amenable $L^2$ -signatures, Ozsváth-Szabó d-invariants and Némethi’s result on Heegaard Floer homology of Seifert 3-manifolds. In an appendix, we present a general formulation of the notion of primary decomposition.

scholarly journals Primary decomposition and the fractal nature of knot concordance

2010 ◽  
Vol 351 (2) ◽  
pp. 443-508 ◽  
Author(s):  
Tim D. Cochran ◽  
Shelly Harvey ◽  
Constance Leidy
Keyword(s):  
Primary Decomposition ◽  
Fractal Nature ◽  
Knot Concordance

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann

John von Neumann

2004 ◽  
Vol 174 (12) ◽  
pp. 1371 ◽  
Author(s):  
Mikhail I. Monastyrskii
Keyword(s):  
John Von Neumann ◽  
Von Neumann
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