Mathematics – Algebraic Topology
Scientific paper
2007-10-31
Mathematics
Algebraic Topology
99 pages, in Russian
Scientific paper
We develop a geometric approach to stable homotopy groups of spheres in the spirit of the work of Pontrjagin and Rokhlin. A new proof of the Hopf Invariant One Theorem by J.F.Adams is obtained in all dimensions except 15 and 31. To prove that the stable Hopf invariant H: \Pi_n \to Z/2 vanishes for n>31, we apply methods of geometric topology. The Pontrjagin-Thom construction along with Hirsch's compression lemma identify every \alpha \in \Pi_n with the framed bordism class of a framed immersion of a closed n-manifold into R^{n+k}, for any given k>0. Its self-intersection M projects to an immersion f: M \to R^n which is framed by k copies of a line bundle \kappa. It is well-known that H(\alpha) =
No associations
LandOfFree
Geometric approach towards stable homotopy groups of spheres. The Hopf invariant 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 Geometric approach towards stable homotopy groups of spheres. The Hopf invariant, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric approach towards stable homotopy groups of spheres. The Hopf invariant will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-14100