General Small Cancellation Theory

General Small Cancellation Theory (172 pages) recently appeared in the International Journal of Algebra and Computation. Because of its length, I have also made it available part by part.

• Introduction (7 pages) This file contains a statement of the main theorem, an overview of the key new concepts, and a table of contents
• Part I Cones (29 pages) This part introduces the notion of a cone complex and the partially ordered sets which are used to describe them.
• Part II Relators (28 pages) - This part introduces the general notion of a relator which is used throughout.
• Part III Constructions (30 pages) - This part extends the standard construction and the Cayley complex to these general relators and general presentations.
• Part IV Small Cancellation Theory (26 pages) This part is the heart of the paper. It defines general small cancellation theory in axiomatic form and shows that the standard results of small cancelllation theory still hold in this expanded arena.
• Part V Consequences (48 pages) - This part proves the more detailed consequences of the axioms, including the asphericity result and the limitations on the structure of the finite subgroups.