Introduction: The Main Problem Prerequisites. What background is needed for reading this text? Chiefly, a knowledge of piecewise linear topology. For many years the standard reference in that area has been the text Introduction to Piecewise-Linear Topology, by C. P. Rourke and B. J. Sanderson (1972), and we assume familiarity with much of their book. To be honest, that book presumes extensive understanding of both general and algebraic topology as a con- sequence we implicitly are assuming those subjects as well. In an attempt to limit our presumptions, we specifically shall take as granted the results from two fairly standard texts on general and algebraic topology, both by J. R. Munkres—namely, his Topology: Second Edition (2000) and Elements of Algebraic Topology (1984), each of which can be treated quite effectively in a year-long graduate course. Unfortunately, even those three texts turn out to be insuﬃcient for all our needs. The purpose of the initial Chapter 0, the Prequel, is to correct that deficiency. Basic Terminology. The notation laid out in this subsection should be familiar to those who have read Rourke and Sanderson’s text. Neverthe- less, we spell out the essentials needed to fully understand the forthcoming discussion of the primary issues addressed in this book. Here R denotes the set of real numbers and Rn denotes n-dimensional Euclidean space, the Cartesian product of n copies of R. For 1 ≤ k n we regard Rk as included in Rn in the obvious way, as the subset containing all points whose final (n − k)-coordinates are all equal to zero. xiii

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2009 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.