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Thanks.

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Thanks.

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quasar987

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Thanks-- I should have clarified. I'm interested in the algebraic topological definition and proof. Here, the Hopf invariant is the integer h such that [tex] \alpha \smile \alpha = h\beta[/tex] where [tex]\alpha[/tex] generates the 2-d cohomology and [tex]\beta[/tex] generates the 4-d cohomology of the mapping cone of [tex]f:S^3 \to S^2[/tex]. The degree of [tex]g:S^3\to S^3[/tex] is the integer d such that [tex] f_* \gamma = d\gamma[/tex] where [tex]\gamma[/tex] generates the 3-d homology of S^3.

Unfortunately, I have very little intuition/feel for algebraic topology and I much prefer the differential forms and differential topology analogs.

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