A note on 0-bipolar knots of concordance order two

2017/12/27 by Wenzhao Chen, Chen, Wenzhao
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.1712.09622

Abstract

Let T be the group of smooth concordance classes of topologically slice knots, and \0\⊂⋯⊂ T_n+1\subsetT_n⊂ ⋯⊂ T₀⊂ T be the bipolar filtration. In this paper, we show that a proper collection of the knots employed by Hedden, Kim, and Livingston to prove ℤ₂^∞ < T can be used to see ℤ₂^∞ < T₀/T₁.

Related

• The bipolar filtration of topologically slice knots
• One-bipolar topologically slice knots and primary decomposition
• Knot Floer Filtration Classes of Topologically Slice Knots
• Primary decomposition in the smooth concordance group of topologically slice knots
• On the concordance orders of knots