Small cancellation theory and its various generalizations have proven to be powerful tools in the study of infinite groups, particularly for the construction of examples of groups exhibiting specific properties. In this article we derive statements which are similar to but significantly stronger than the usual small cancellation formulations. These stronger results are presented using the notio...

We establish a connection between the geometric methods developed in the combinatorial theory of small cancellation and the propositional resolution calculus. We define a precise correspondence between resolution proofs in logic and diagrams in small cancellation theory, and as a consequence, we derive that a resolution proof is a 2dimensional process. The isoperimetric function defined on diag...

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from

We show that the Wirtinger presentation of a prime alternating link group satisfies a generalized small cancellation condition. This gives a simplification of Weinbaum’s solution to the word and conjugacy problems for these groups, which extends to finite sums of alternating links.

Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.

It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaumé and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice spacing (i.e. close to the classical continuum limit). As a consequence, the continuum anomaly cancellation condition dabc R = 0 is seen to be a necessary (alt...