The bipolar filtration of topologically slice knots

2017/10/21 by Jae Choon Cha, Cha, Jae Choon, Min Hoon Kim +1 · 1 citation
Mathematics · #57M25 #57M27 #57N13 #57N70 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1710.07803

openalex publication_date 2017/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of deeper structures in the smooth concordance group of topologically slice knots. We show that the graded quotient of the bipolar filtration of topologically slice knots has infinite rank at each stage greater than one. To detect nontrivial elements in the quotient, the proof simultaneously uses higher order amenable Cheeger-Gromov L² ρ-invariants and infinitely many Heegaard Floer correction term d-invariants.

Cited by

• Smoothly slice knots with smoothly non-approximable topological slice discs

Related

• One-bipolar topologically slice knots and primary decomposition
• A note on 0-bipolar knots of concordance order two
• Knot Floer Filtration Classes of Topologically Slice Knots
• Primary decomposition in the smooth concordance group of topologically slice knots
• Knot concordance and Blanchfield duality