 
Summary: A General Small Cancellation Theory
Jonathan P. McCammond
September 16, 1999
Abstract
In this article a generalized version of small cancellation theory is de
veloped which is applicable to specific types of highdimensional simplicial
complexes. The usual results on small cancellation groups are then shown
to hold in this new setting with only slight modifications. For example, ar
bitrary dimensional versions of the PoincarŽe construction and the Cayley
complex are described.
0.1 Main Theorems
In this article a generalized version of traditional small cancellation theory is
developed which is applicable to specific types of highdimensional simplicial
complexes. The usual results on small cancellation groups are then shown to
hold in this new setting with only slight modifications. The main results derived
for this general small cancellation theory are summarized below in Theorem A.
The notions of general relators, Cayley categories, and general small cancellation
presentations are being introduced here, and will be defined in the course of the
article.
Theorem A If G = AR is a general small cancellation presentation with
