The Index of Manifolds with Toral Actions and Geometric Interpretations of the ... (..., (S1, Mn)) Invariant of Atiyah and Singer.
Inventiones mathematicae, Tome 15 (1971), pp. 53-66.

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@article{IM_1971__15_142120,
     author = {Frank Raymond and Katsuo Kawakubo},
     title = {The {Index} of {Manifolds} with {Toral} {Actions} and {Geometric} {Interpretations} of the ... (..., {(S1,} {Mn))} {Invariant} of {Atiyah} and {Singer.}},
     journal = {Inventiones mathematicae},
     pages = {53--66},
     publisher = {mathdoc},
     volume = {15},
     year = {1971},
     zbl = {0243.57017},
     url = {http://geodesic.mathdoc.fr/item/IM_1971__15_142120/}
}
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Frank Raymond; Katsuo Kawakubo. The Index of Manifolds with Toral Actions and Geometric Interpretations of the ... (..., (S1, Mn)) Invariant of Atiyah and Singer.. Inventiones mathematicae, Tome 15 (1971), pp. 53-66. http://geodesic.mathdoc.fr/item/IM_1971__15_142120/