The piecewise linear surface signature is injective: it characterizes surfaces up to translation and thin homotopy, generalizing Chen's path signature theorem.
The A ∞ de Rham Theorem and Integration of Representations up to Homotopy
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Thin homotopy and the signature of piecewise linear surfaces
The piecewise linear surface signature is injective: it characterizes surfaces up to translation and thin homotopy, generalizing Chen's path signature theorem.