Polyhedral homotopy-spheres

John R. Stallings
1960 Bulletin of the American Mathematical Society  
It has been conjectured that a manifold which is a homotopy sphere is topologically a sphere. This conjecture has implications, for example, in the theory of differentiate structures on spheres (see, e.g., [3, p. 33]). Here I shall sketch a proof of the following theorem: Let M be a piecewise-linear manifold of dimension n^7, which has the same homotopy-type as the n-sphere S n . Then there is a piecewiselinear equivalence of M-{point} with euclidean n-space\ in particular, M is topologically
more » ... is topologically equivalent to S n . This theorem is not the best possible, for C. Zeeman has been able to refine the method presented here so as to prove the same theorem for n^5.
doi:10.1090/s0002-9904-1960-10511-3 fatcat:ubzlpqkyb5gndm3nb2ej5jjmji