Homotopy groups of PL-embedding spaces. II

Lawrence Stanislaus Husch, Jr.

Vol. 38 (1971), No. 3, 653–655

DOI: 10.2140/pjm.1971.38.653

Abstract

Theorem. For i ≦ m− 2 and n ≦ m − 3,π_iPL(Sⁿ,S^m) is isomorphic to π_iV _m,n^PL, the homotopy groups of the PL-Stiefel manifold of n-planes in Euclidean m-space.

E. C. Zeeman [10] conjectured that the homotopy groups, π_iPL(Sⁿ,S^m),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