On the degree 2 map for a sphere

Details On the degree 2 map for a sphere On the degree 2 map for a sphere

2005-09-22

arxiv.org/abs/math/0509533v1

Mathematics

Algebraic Topology

Scientific paper

The purpose of this article is to compare the two self-maps of $\Omega^kS^{2n+1}$ given by $\Omega^k[2]$ the $k$-fold looping of a degree 2 map and $\Psi^k(2)$ the H-space squaring map. The main results give that in case $2n+1 \neq 2^j-1$, these maps are frequently not homotopic and also that their homotopy theoretic fibres are not homotopy equivalent. The methods are a computation of an unstable secondary operation constructed by Brown and Peterson in the first case and the Nishida relations in the second case. One question left unanswered here is whether the maps $\Omega^{2n+1}[2]$ and $\Psi^{2n+1}(2)$ are homotopic on the level of $\Omega^{2n+1}_0S^{2n+1}$. A natural conjecture is that these two maps are homotopic.

Affiliated with

Also associated with

No associations

Rating

On the degree 2 map for a sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the degree 2 map for a sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the degree 2 map for a sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-71188