On the image of the unstable Boardman map
Hadi Zare

TL;DR
This paper investigates the image of the unstable Boardman map at prime 2, identifying cases where the map's image is trivial or non-trivial, especially relating to H-space structures and Hopf invariant one elements.
Contribution
It determines the image of the unstable Boardman map for specific cases at prime 2, highlighting when the image is trivial or non-trivial based on space structures.
Findings
Image is trivial in most cases.
Non-trivial image occurs with H-space structures or Hopf invariant one elements.
Results depend on the relationships between m, n, and l.
Abstract
We consider the `unstable Boardman map' (homomorphism if ) defined by . We work at the prime , with , and determine the image for various in the following cases : (1) and arbitrary; (2) and . We observe that in most of the cases the image is trivial with the exceptions corresponding to the cases when either there is a (commutative) -space structure on or there is a Hopf invariant one element.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Algebra and Geometry
