Invariants via word for curves and fronts

Details Invariants via word for curves and fronts Invariants via word for curves and fronts

2007-05-03

arxiv.org/abs/0705.0412v2

Mathematics

Geometric Topology

26pages

Scientific paper

We construct the infinite sequence of invariants for curves in surfaces by using word theory that V. Turaev introduced. For plane closed curves, we add some extra terms, e.g. the rotation number. From these modified invariants, we get the Arnold's basic invariants and some other invariants. We also express how these invariants classify plane closed curves. In addition, we consider other classes of plane curves: long curves and fronts.

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