An obstruction to extending isotopies of piecewise linear manifolds

Ewing L. Lusk

Vol. 56 (1975), No. 2, 575–579

DOI: 10.2140/pjm.1975.56.575

Abstract

Let F : M ×Iⁿ → Q×Iⁿ be an n-isotopy (not necessarily PL) of a compact PL m-manifold M in a PL q-manifold Q, and let G : Q × Iⁿ → Q × Iⁿ be an ambient isotopy of Q which covers F on Q × ∂Iⁿ. If m ≦ q − 3 there is in π_n PL(M,Q) an obstruction to finding an ambient isotopy of Q, isotopic to G, which covers F and agrees with G on Q × ∂Iⁿ.

Mathematical Subject Classification

Primary: 57C40

Milestones

Received: 1 February 1973

Published: 1 February 1975