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

Keywords
knots, $RP^2$, plane curves, singular curves
Mathematical Subject Classification 2000
Primary: 53A04
Secondary: 14H50
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Publication
Received: 2 February 2006
Accepted: 2 May 2006
Published: 19 November 2006
Authors
Abigail Thompson
Mathematics Department
University of California
Davis, CA 95616
USA