Geometric proof of the fact that product of two elements of odd order in image of $J$ is zero.












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I want to prove that product of two elements of odd order in image of $J$ is zero. I tried to approach this via the Thom-Pontryagin condition. So the image of $J$ just corresponds to spheres with framing. Now I am not sure how to prove that the product is zero when the framings have odd order. So I am looking for a reference which does this in a geometric way. Thanks!










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    I want to prove that product of two elements of odd order in image of $J$ is zero. I tried to approach this via the Thom-Pontryagin condition. So the image of $J$ just corresponds to spheres with framing. Now I am not sure how to prove that the product is zero when the framings have odd order. So I am looking for a reference which does this in a geometric way. Thanks!










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      I want to prove that product of two elements of odd order in image of $J$ is zero. I tried to approach this via the Thom-Pontryagin condition. So the image of $J$ just corresponds to spheres with framing. Now I am not sure how to prove that the product is zero when the framings have odd order. So I am looking for a reference which does this in a geometric way. Thanks!










      share|cite|improve this question













      I want to prove that product of two elements of odd order in image of $J$ is zero. I tried to approach this via the Thom-Pontryagin condition. So the image of $J$ just corresponds to spheres with framing. Now I am not sure how to prove that the product is zero when the framings have odd order. So I am looking for a reference which does this in a geometric way. Thanks!







      homotopy-theory stable-homotopy-theory






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      asked Dec 2 '18 at 18:44









      happymath

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