3,927 research outputs found
-based Mahowald invariants
The -primary homotopy -family, defined as the collection of
Mahowald invariants of Mahowald invariants of , , is an infinite
collection of periodic elements in the stable homotopy groups of spheres. In
this paper, we calculate -based approximations to this family.
Our calculations combine an analysis of the Atiyah-Hirzebruch spectral sequence
for the Tate construction of with trivial -action and
Behrens' filtered Mahowald invariant machinery.Comment: 52 pages, 41 figures. Comments welcome
Symmetries of exotic spheres via complex and quaternionic Mahowald invariants
We deduce the existence of smooth - and -actions on certain
exotic spheres using complex and quaternionic analogues of the Mahowald
{(root)} invariant. In particular, we prove that the complex (respectively,
quaternionic) Mahowald invariant takes an element of represented by a
homotopy sphere to an element {of } represented by
another homotopy sphere equipped with a smooth -
(respectively, -) action with fixed points the original homotopy sphere
. This work is motivated by results of Stolz
on the classical Mahowald invariant and smooth -actions on homotopy
spheres.Comment: 19 pages. Comments welcome
Choosing the Right Consultant
The church in North America is in decline. Research indicates that many churches are not growing or even considered “healthy.” More and more churches are addressing their declining attendance through hiring consultants to identify areas of growth and improvement. The key is finding the right consultant or consulting firm for the needs of the local church. This article seeks to help the local church ask the right questions when selecting a consultant or consulting firm
Algebraic slice spectral sequences
For certain motivic spectra, we construct a square of spectral sequences relating the effective slice spectral sequence and the motivic Adams spectral sequence. We show the square can be constructed for connective algebraic K-theory, motivic Morava K-theory, and truncated motivic Brown-Peterson spectra. In these cases, we show that the -motivic effective slice spectral sequence is completely determined by the -Bockstein spectral sequence. Using results of Heard, we also obtain applications to the Hill-Hopkins-Ravenel slice spectral sequences for connective Real K-theory, Real Morava K-theory, and truncated Real Brown-Peterson spectra. <br
-periodic motivic homotopy over prime fields
We compute the motivic stable homotopy groups of a variant of the connective
image-of- spectrum over prime fields of characteristic not two. Together
with the analogous computation over algebraically closed fields, this yields
information about -periodic motivic stable homotopy groups over arbitrary
base fields of characteristic not two.Comment: 30 pages, 16 figures. Comments welcome
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