Algebraic & Geometric Topology

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

Abigail Thompson

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

Permanent link to this document
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

Keywords
knots $RP^2$ plane curves singular 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


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