Classification of simply connected six-dimensional spin manifolds

In this paper we present a differential and homotopic classification of simply connected closed six-dimensional smooth manifolds with a zero two-dimensional Stiefel-Whitney class. The method we employ consists in reducing the classificational problems of calculating the groups of spin bordisms of certain Eilenberg-MacLane spaces. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 45, pp. 71–74, 1974.