Geodesic
Structure in the bipolar filtration of topologically slice knots
Cochran, Tim D1 ; Horn, Peter D2
1Department of Mathematics MS-136, Rice University, PO Box 1892, Houston, TX 77251-1892, USA
2Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, NY 13244-1150, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 415-428
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Let T be the group of smooth concordance classes of topologically slice knots and suppose

is the bipolar filtration of T. We show that T0∕T1 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.

DOI : 10.2140/agt.2015.15.415
Classification : 57M25, 57N70
Keywords: knot, topologically slice, bipolar filtration

Cochran, Tim D  1   ; Horn, Peter D  2

1 Department of Mathematics MS-136, Rice University, PO Box 1892, Houston, TX 77251-1892, USA
2 Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, NY 13244-1150, USA 
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Cochran, Tim D; Horn, Peter D. Structure in the bipolar filtration of topologically slice knots. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 415-428. doi: 10.2140/agt.2015.15.415

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