#### Volume 6, issue 5 (2006)

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Invariants of curves in $RP^2$ and $R^2$

### Abigail Thompson

Algebraic & Geometric Topology 6 (2006) 2175–2186
 arXiv: math.GT/0602003
##### Abstract

There is an elegant relation found by Fabricius-Bjerre [Math. Scand 40 (1977) 20–24] among the double tangent lines, crossings, inflections points, and cusps of a singular curve in the plane. We give a new generalization to singular curves in $R{P}^{2}$. We note that the quantities in the formula are naturally dual to each other in $R{P}^{2}$, and we give a new dual formula.

##### Keywords
knots, $RP^2$, plane curves, singular curves
Primary: 53A04
Secondary: 14H50