574 research outputs found
The triviality of the 61-stem in the stable homotopy groups of spheres
We prove that the 2-primary is zero. As a consequence, the
Kervaire invariant element is contained in the strictly defined
4-fold Toda bracket .
Our result has a geometric corollary: the 61-sphere has a unique smooth
structure and it is the last odd dimensional case - the only ones are and .
Our proof is a computation of homotopy groups of spheres. A major part of
this paper is to prove an Adams differential . We prove this
differential by introducing a new technique based on the algebraic and
geometric Kahn-Priddy theorems. The success of this technique suggests a
theoretical way to prove Adams differentials in the sphere spectrum inductively
by use of differentials in truncated projective spectra.Comment: 67 pages, minor changes, accepted versio
The special fiber of the motivic deformation of the stable homotopy category is algebraic
For each prime , we define a -structure on the category
of harmonic
-motivic left module spectra over , whose
MGL-homology has bounded Chow-Novikov degree, such that its heart is equivalent
to the abelian category of -completed -comodules that are
concentrated in even degrees. We prove that
is equivalent to
as stable
-categories equipped with -structures.
As an application, for each prime , we prove that the motivic Adams
spectral sequence for , which converges to the motivic
homotopy groups of , is isomorphic to the algebraic
Novikov spectral sequence, which converges to the classical Adams-Novikov
-page for the sphere spectrum . This isomorphism of
spectral sequences allows Isaksen and the second and third authors to compute
the stable homotopy groups of spheres at least to the 90-stem, with ongoing
computations into even higher dimensions.Comment: Accepted version, 85 page
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Carbon Monoxide Oxidation Promoted by Surface Polarization Charges in a CuO/Ag Hybrid Catalyst.
Composite structures have been widely utilized to improve material performance. Here we report a semiconductor-metal hybrid structure (CuO/Ag) for CO oxidation that possesses very promising activity. Our first-principles calculations demonstrate that the significant improvement in this system's catalytic performance mainly comes from the polarized charge injection that results from the Schottky barrier formed at the CuO/Ag interface due to the work function differential there. Moreover, we propose a synergistic mechanism underlying the recovery process of this catalyst, which could significantly promote the recovery of oxygen vacancy created via the M-vK mechanism. These findings provide a new strategy for designing high performance heterogeneous catalysts
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