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A composite map in the stable homotopy groups of spheres
-
Xiugui Liu
Published/Copyright:
March 1, 2013
Abstract.
In 2001, J. Lin detected a non-trivial element 
in the
stable homotopy group 
of the
sphere spectrum S for 
at the prime greater than three.
In the stable homotopy group 
of the Smith–Toda spectrum 
, X. Liu constructed an essential
element 
for 
at the prime greater than three.
Let 
denote the Spanier–Whitehead dual of the generator
,
which defines the 
-element 
. Let
. In this paper, we show that
the composite maps 
and 
are
non-trivial, where 
and 
. In the
Adams–Novikov spectral sequence, the maps and
are represented by
and
,
respectively. Here 
denotes the well-known element in
.
Received: 2010-07-03
Revised: 2011-01-13
Published Online: 2013-03-01
Published in Print: 2013-03-01
© 2013 by Walter de Gruyter Berlin Boston
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- Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary
- A composite map in the stable homotopy groups of spheres
- Length functions, multiplicities and algebraic entropy
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Keywords for this article
Adams spectral sequence;
May spectral sequence;
Adams–Novikov spectral sequence
Articles in the same Issue
- Masthead
- Non-Lipschitz flow of the nonlinear Schrödinger equation on surfaces
- Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary
- A composite map in the stable homotopy groups of spheres
- Length functions, multiplicities and algebraic entropy
- On the Eisenstein cohomology of odd orthogonal groups
- Complex Osserman Kähler manifolds in dimension four
- Mixed multiplicities of multigraded modules
- On the number of maximal chain transitive sets in fiber bundles
- 2-primary factorizations of power maps through the double suspension
- Imprecise probabilities, bets and functional analytic methods in Łukasiewicz logic
