## Algebraic & Geometric Topology

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

Abigail Thompson

#### 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 $RP2$. We note that the quantities in the formula are naturally dual to each other in $RP2$, and we give a new dual formula.

#### Article information

Source
Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2175-2186.

Dates
Accepted: 2 May 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796634

Digital Object Identifier
doi:10.2140/agt.2006.6.2175

Mathematical Reviews number (MathSciNet)
MR2263063

Zentralblatt MATH identifier
1128.53010

Subjects
Primary: 53A04: Curves in Euclidean space
Secondary: 14H50: Plane and space curves

#### Citation

Thompson, Abigail. Invariants of curves in $RP^2$ and $R^2$. Algebr. Geom. Topol. 6 (2006), no. 5, 2175--2186. doi:10.2140/agt.2006.6.2175. https://projecteuclid.org/euclid.agt/1513796634