Geodesic
A Geometrical Proof of Browder's Result on the Vanishing of the Kervaire Invariant
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 46-51

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The Kervaire invariant is a $Z/2$-invariant of framed manifolds of dimension $n=4k+2$. W. Browder proved that this invariant necessarily vanishes if $n+2$ is not a power of 2. We give a geometrical proof of this result using a characterization of the Kervaire invariant in terms of multiple points of immersions. 
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     author = {P. M. Akhmet'ev and P. J. Eccles},
     title = {A {Geometrical} {Proof} of {Browder's} {Result} on the {Vanishing} of the {Kervaire} {Invariant}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {46--51},
     publisher = {mathdoc},
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     year = {1999},
     language = {ru},
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P. M. Akhmet'ev; P. J. Eccles. A Geometrical Proof of Browder's Result on the Vanishing of the Kervaire Invariant. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 46-51. http://geodesic.mathdoc.fr/item/TM_1999_225_a3/