Vol. 38, No. 3, 1971

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Homotopy groups of PL-embedding spaces. II

Lawrence Stanislaus Husch, Jr.

Vol. 38 (1971), No. 3, 653–655
Abstract

Theorem. For i m2 and n m 3iPL(Sn,Sm) is isomorphic to πiV m,nPL, the homotopy groups of the PL-Stiefel manifold of n-planes in Euclidean m-space.

E. C. Zeeman [10] conjectured that the homotopy groups, πiPL(Sn,Sm),m n+i+3, of the space of PL-embeddings of the n-sphere into the m-sphere were trivial. As indicated in [4], results of M. C. Irwin [5] and C. Morlet [7] can be used to verify this conjecture. In the theorem above, we generalize this result.

Mathematical Subject Classification
Primary: 57C35
Milestones
Received: 6 November 1969
Published: 1 September 1971
Authors
Lawrence Stanislaus Husch, Jr.