Geodesic
The actions of a circumference on smooth odd-dimensional spheres
Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 401-408.

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The $J$-invariant of a smooth structure on an odd-dimensional sphere is constructed, which allows us to obtain information on smooth structures on a sphere with free action of a circumference and, in particular, yields complete information when the sphere is of dimension seven. 
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     author = {F. A. Bogomolov},
     title = {The actions of a circumference on smooth odd-dimensional spheres},
     journal = {Matemati\v{c}eskie zametki},
     pages = {401--408},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a0/}
}
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F. A. Bogomolov. The actions of a circumference on smooth odd-dimensional spheres. Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 401-408. http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a0/