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The small-cancellation conditions C(lambda) and C prime(lambda)
Definition
Fix a real number with , and let be a symmetrised relator set.
The set satisfies when every piece occurring in a relator satisfies
It satisfies when, whenever a relator is written as a concatenation of pieces , one has
Here piece means the notion fixed in A piece is a common initial segment occurring in two distinct places of a symmetrised relator set. The strict inequality in is part of the convention used on this page.
Depends on
Used by
- An overlap of exactly one sixth shows that the strict C prime(1/6) inequality is not cosmetic Counterexample
- A concrete relator set with its pieces and a direct C prime(1/6) check Example
- FALSE: C prime(1/6) means every relator has length at most six False statement
- C prime(lambda) implies C(lambda) Lemma
- Reduced C prime(1/6) diagrams satisfy the standard combinatorial curvature count Lemma
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- GAP SmallCancellation manual, Chapter 1: Small Cancellation Theory — the classical conditions (standard reference, not scraped)
- Jay Williams, Universal Countable Borel Quasi-Orders (standard reference, not scraped)
- Nicholas Touikan, An Introduction to Combinatorial and Geometric Group Theory, Section 3.5 (standard reference, not scraped)
- Clara Löh, Geometric Group Theory: An Introduction, Section 7.4.1 (standard reference, not scraped)