Algebraic & Geometric Topology

Structure in the bipolar filtration of topologically slice knots

Tim D Cochran and Peter D Horn

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Abstract

Let T be the group of smooth concordance classes of topologically slice knots and suppose

Tn+1 Tn T2 T1 T0 T

is the bipolar filtration of T. We show that T0T1 has infinite rank, even modulo Alexander polynomial one knots. Recall that knots in T0 (a topologically slice 0–bipolar knot) necessarily have zero τ–, s– and ϵ–invariants. Our invariants are detected using certain d–invariants associated to the 2–fold branched covers.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 415-428.

Dates
Received: 3 March 2014
Revised: 4 August 2014
Accepted: 5 August 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510840917

Digital Object Identifier
doi:10.2140/agt.2015.15.415

Mathematical Reviews number (MathSciNet)
MR3325742

Zentralblatt MATH identifier
1318.57005

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57N70: Cobordism and concordance

Keywords
knot topologically slice bipolar filtration

Citation

Cochran, Tim D; Horn, Peter D. Structure in the bipolar filtration of topologically slice knots. Algebr. Geom. Topol. 15 (2015), no. 1, 415--428. doi:10.2140/agt.2015.15.415. https://projecteuclid.org/euclid.agt/1510840917


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