Invariants of curves in RP2 and R2

Thompson, Abigail

doi:10.2140/agt.2006.6.2175

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

Abigail Thompson

Algebraic & Geometric Topology 6 (2006) 2175–2186

DOI: 10.2140/agt.2006.6.2175

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

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

Volume 6, issue 5 (2006)