Amenable L2-theoretic methods and knot concordance

Cha, Jae Choon

doi:10.48550/arxiv.1010.1058

Cited by 1 publication

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We can also relate Z (p) -homology positivity to amenable von Neumann ρ-invariants, following the idea of [CHH13, Section 5] and using techniques of [Cha10]. We discuss this in more detail in Appendix B (see Theorem B.1).…”

Section: Obstructions To Homology 0-and 1-positivitymentioning

confidence: 99%

“…Our proof is a combination of the idea of its homotopy n-positive analogue (see [CHH13,Theorem 5.8]) and the technique for amenable L 2 -invariants in [Cha10].…”

Section: Appendix B Amenable Von Neumann ρ-Invariants and N-positivitymentioning

confidence: 99%

“…We remark that a more general case of the mixed-coefficient derived series was defined in [Cha10]. It should also be noted that our Z (p) -coefficient derived series is not equal to the Z p -coefficient analogue, namely the series obtained by replacing Z (p) with Z p , which appeared in the literature as well; P n G/P n+1 G is the maximal abelian quotient of P n G which has no torsion coprime to p, while the corresponding quotient of the Z p -coefficient analogue is the maximal abelian quotient which is a Z p -vector space.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Covering link calculus and the bipolar filtration of topologically slice links

Choon

Powell

2014

Geom. Topol.

Self Cite

View full text Add to dashboard Cite

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. The bipolar filtration introduced by T Cochran, S Harvey and P Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1-bipolar knots which are not 2-bipolar. For knots, this is the highest known level at which the filtration does not stabilize. For the case of links with two or more components, we prove that the filtration does not stabilize at any level: for any n, there are topologically slice links which are n-bipolar but not .n C 1/-bipolar. In the proof we describe an explicit geometric construction which raises the bipolar height of certain links exactly by one. We show this using the covering link calculus. Furthermore we discover that the bipolar filtration of the group of topologically slice string links modulo smooth concordance has a rich algebraic structure. 57M25, 57N70

show abstract

Section: Obstructions To Homology 0-and 1-positivitymentioning

confidence: 99%

“…Our proof is a combination of the idea of its homotopy n-positive analogue (see [CHH13,Theorem 5.8]) and the technique for amenable L 2 -invariants in [Cha10].…”

Section: Appendix B Amenable Von Neumann ρ-Invariants and N-positivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation