Consider a closed curve in the plane that does not intersect itself; by
the Jordan Curve Theorem, it bounds a distorted disk. Now consider a
closed curve that intersects itself, perhaps several times. Is it the
boundary of a distorted disk that overlaps itself? If it is, is that
distorted disk essentially unique? The question of when an immersion of
the circle can be extended to an immersion of a disk has been studied by
several people, notably Titus [C. J. Titus, The combinatorial
topology of analytic functions on the boundary of a disk, Acta Math. 106
(1961), 45-64.] and Blank [S. J. Blank, Extending immersions of the
circle, Dissertation, Brandeis University, Mass. (1967)]. I will discuss
their work and then I will develop combinatorial techniques for answering
these questions.
R E F R E S H M E N T S
4:00 To 4:25 PM
Kenneth W. Anderson
Memorial Reading Room
