- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2016
2
Geometric filtrations of string links and homology cylinders
James
Conant
University of Tennessee, KNOXVILLE, UNITED STATES
Robert
Schneiderman
Lehman College, City University of New York, BRONX, UNITED STATES
Peter
Teichner
Max Planck Institut für Mathematik, BONN, GERMANY
Artin representation, clasper, homology cylinder, Johnson filtration, string link, Whitney tower, Y-filtration
We show that the group of string links modulo order $n$ twisted Whitney tower concordance is an extension of the image of the nilpotent Artin representation by a finite 2-group. Moreover, this 2-group is generated by band sums of iterated Bing-doubles of any string knot with nonzero Arf invariant. We also analyze the Goussarov–Habiro clasper fi ltration of the group of 3-dimensional homology cylinders modulo homology cobordism, importing techniques from our work on Whitney towers to improve on results of J. Levine. In particular, we classify the graded group associated to the Goussarov–Habiro fi ltration in all orders except $4n + 1$. In this last case, it is classi fied up to unknown 2-torsion with a precise upper bound. These calculations confi rm conjectures of Levine in the even cases, and improve on his conjectures in the odd cases. In the last section of this paper we connect the settings of string links and homology cylinders by analyzing a geometric map, originally formulated by N. Habegger.
Manifolds and cell complexes
281
328
10.4171/QT/77
http://www.ems-ph.org/doi/10.4171/QT/77