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Whitney tower concordance
of classical links
James Conant, Rob Schneiderman and Peter Teichner |
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Geometry & Topology 16 (2012) 1419–1479
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Abstract |
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This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato–Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the –ball bounded by a link in the –sphere. Applications include computation of the grope filtration and new geometric characterizations of Milnor’s link invariants. |
Keywords
Whitney tower, grope, link concordance, tree, higher-order
Arf invariant, higher-order Sato–Levine invariant, twisted
Whitney disk
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57Q60
Secondary: 57N10
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References |
Publication
Received: 4 February 2011
Revised: 28 May 2012
Accepted: 28 May 2012
Published: 24 July 2012
Proposed: Rob Kirby
Seconded: Ronald J Stern, David Gabai
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Authors |
| James Conant | |
| Department of Mathematics University of Tennessee Knoxville TN 37996 USA |
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| http://www.math.utk.edu/~jconant/ | |
| Rob Schneiderman | |
| Department of Mathematics and
Computer Science Lehman College, CUNY Bronx NY 10468-1589 USA |
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| http://comet.lehman.cuny.edu/schneiderman/ | |
| Peter Teichner | |
| Department of Mathematics University of California, Berkeley Berkeley CA 94720-3840 USA |
Max-Planck Institut für Mathematik, Bonn, Germany |
| http://math.berkeley.edu/~teichner/ | |
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