Piecewise linear homeomorphisms

Abstract

Let K and L be complexes. We recall, from Section 0, that a homeomorphism

$$f:|K| \leftrightarrow |L|$$

is piecewise linear (relative to K and L) if there is a subdivision K ₁ of K such that for each σ ∈ K ₁, f|σ maps σ linearly into a simplex of L. “PL” stands for piecewise linear, and “PLH” stands for PL homeomorphism, or PL homeomorphic. If K ₁ is a subdivision of K, then we write K ₁ < K.