منابع مشابه
On the Hopf-toda Invariant
0. Introduction. One line of attack on the problem of computing the unstable homotopy groups of spheres is to attempt to construct the elements whose reduced product filtration exceeds 1. The classical Hopf construction associates with a map Sm x S'"1 -> S" of type (a,/?) an element of 7tm+I(S"+1). The indeterminacy of the construction is the suspension subgroup in the sense that the elements a...
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This paper will discuss the Adams-Atiyah solution to the Hopf invariant problem. We will first define and prove some identities concerning the Adams operations. Then we will look at the proof of the ordinary Hopf invariant one problem. Finally we will look at some results concerning the pth cup power mod p and the mod p version of the Hopf invariant problem.
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This paper will establish that there are only four sphere bundles over spheres that are in turn spheres. The first sections consist of introductions to fiber bundles, the basics of cohomology, and the Hopf invariant, while the rest of the paper establishes the Gysin sequence and uses it to prove the final theorem. Some prior knowledge of basic homotopy theory, homology, and CW complexes is assu...
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Let ƒ: N —• M be a C°° map of oriented compact manifolds, and let L be an oriented closed submanifold of codimension q > 1 in M. If w is a closed form Poincaré dual to L, we show that f~L, with multiplicities counted, is Poincaré dual to ƒ *w in N and is even meaningful on a "secondary" level. This leads to generalized versions of the Hopf invariant, the Hopf index theorem and the Bezout theore...
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ژورنال
عنوان ژورنال: Topology
سال: 1970
ISSN: 0040-9383
DOI: 10.1016/0040-9383(70)90048-0