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The universal templates of Ghrist

Author: R. F. Williams
Journal: Bull. Amer. Math. Soc. 35 (1998), 145-156
MSC (1991): Primary 57-XX
MathSciNet review: 1602073
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Abstract: This is a report on recent work of Robert Ghrist in which he shows that universal templates exist. Put another way, there are many structurally stable flows in the 3-sphere, each of which has periodic orbits representing every knot type. This answers a question raised originally by Mo Hirsch and popularized by the contrary conjecture by Joan Birman and the present author.

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Additional Information

R. F. Williams
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712-1082
Address at time of publication: The Institute for Advanced Study, Princeton, New Jersey 08540

Received by editor(s): June 3, 1997
Received by editor(s) in revised form: August 10, 1997, and January 21, 1998
Additional Notes: Supported in part by a grant from the National Science Foundation.
Thanks to Robert Ghrist for his help, in particular for help in drawing the figures.
We thank the Mathematics Department of Montana State University for their hospitality.
Article copyright: © Copyright 1998 American Mathematical Society

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