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On Smoothing Proper Knots
by
Ollie Nanyes
Bradley University
A proper knot is a proper embedding of the real line into an open 3-manifold. By ``proper map'', we mean that the inverse image of a compact set is compact. For exampe, the x-axis in R3 could be thought of as the image of a proper knot. Two proper knots are equivalent if there is a proper isotopy (possibly non-ambient) connecting them. In this talk, we will discuss the problem of ``smoothing'' a proper knot; that is we will give sufficient conditions for a proper knot to be equivalent to a smoothly embedded proper knot. Open questions will also be discussed; for example it is unknown whether there exists any unsmoothable proper knots in any open target 3-manifold.
Date received: January 27, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cady-17.