intersection sequence
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1996 ◽  
Vol 05 (02) ◽  
pp. 137-144 ◽  
Author(s):  
GRANT CAIRNS ◽  
DANIEL M. ELTON

C.F. Gauss gave a necessary condition for a word to be the intersection sequence of a closed normal planar curve and he gave an example which showed that his condition was not sufficient. Since then several authors have given algorithmic solutions to this problem. In a previous paper, along the lines of Gauss’s original condition, we gave a necessary and sufficient condition for the planarity of “signed” Gauss words. In this present paper we give a solution to the planarity problem for unsigned Gauss words.


1976 ◽  
Vol 28 (3) ◽  
pp. 589-593
Author(s):  
John R. Martin

A C1-mapping ƒ from the oriented circle S1 into the oriented plane R2 such that f f’ (t) ≠ 0 for all t is called a regular immersion. We call a point p in Im f a double point if f-1(p) is a two element set with the corresponding tangent vectors being linearly independent. A regular immersion which is one-to-one except at a finite number of points whose images are double points is called a normal immersion. The work of Whitney [7], Titus [3] and Verhey [6] shows that the normal immersions form a dense open subset in the space of regular immersions with the usual C1-topology, and can be characterized up to diffeomorphic equivalence by a combinatorial invariant called the intersection sequence.


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