Geodesic
On a paper by Barden
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 70-88

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It is shown that an approach earlier used by the author for classification of closed simply connected 6-mainfolds (reduction to the problem of calculating certain bordism groups) can also be applied to easily obtain the results of Barden (1965) on classification of closed simply connected 5-mainfolds. 
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     author = {A. V. Zhubr},
     title = {On a paper by {Barden}},
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     year = {2001},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a4/}
}
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A. V. Zhubr. On a paper by Barden. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 70-88. http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a4/