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The Generalized Dehn Property does not imply a linear isoperimetric inequality

Owen Baker and Timothy Riley

The Dehn property for a complex is that every non-trivial disk diagram has spurs or shells. It implies a linear isoperimetric inequality. It has been conjectured that the same is true of a more general property which also allows cutcells. We give counterexamples.

Counterexample 2-complex