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Kervaire invariants and
selfcoincidences
Ulrich Koschorke and Duane Randall |
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Geometry & Topology 17 (2013) 621–638
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Abstract |
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Minimum numbers decide, eg, whether a given map from a sphere into a spherical space form can be deformed to a map such that for all . In this paper we compare minimum numbers to (geometrically defined) Nielsen numbers (which are more computable). In the stable dimension range these numbers coincide. But already in the first nonstable range (when ) the Kervaire invariant appears as a decisive additional obstruction which detects interesting geometric coincidence phenomena. Similar results (involving, eg, Hopf invariants taken mod 4) are obtained in the next seven dimension ranges (when ). The selfcoincidence context yields also a precise geometric criterion for the open question whether the Kervaire invariant vanishes on the 126–stem or not. |
Keywords
Kervaire invariant, coincidence, Nielsen number
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Mathematical Subject Classification 2010
Primary: 55M20, 55P40, 55Q15, 55Q25, 57R99
Secondary: 55Q45
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References |
Publication
Received: 9 August 2011
Revised: 9 August 2012
Accepted: 26 September 2012
Published: 9 April 2013
Proposed: Shigeyuki Morita
Seconded: Ralph Cohen, Steve Ferry
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Authors |
| Ulrich Koschorke | |
| FB 6 - Mathematik V Universität Siegen Emmy Noether Campus Walter-Flex-Str. 3 D-57068 Siegen Germany |
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| http://www.math.uni-siegen.de/topologie/ | |
| Duane Randall | |
| Loyola University New Orleans Mathematical Sciences 6363 St. Charles Ave. Campus Box 35 New Orleans, LA 70118 USA |
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