Algebraic & Geometric Topology

Structure in the bipolar filtration of topologically slice knots

Tim D Cochran and Peter D Horn

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

knot topologically slice bipolar filtration


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.

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