Finite-type invariants for curves on surfaces
classification
🧮 math.GT
keywords
invariantscurvesfinite-typesurfacestheoryarnoldboundariesclasses
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This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a higher-order generalisation of a part of Arnold's invariants that are first-order invariants for plane immersed curves. The invariants in this theory are developed using the word theory proposed by Turaev.
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