Flows on supporting all links as orbits

Author:
Robert W. Ghrist

Journal:
Electron. Res. Announc. Amer. Math. Soc. **1** (1995), 91-97

MSC (1991):
Primary 57M25, 58F22; Secondary 58F25, 34C35

MathSciNet review:
1350685

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Abstract: We construct counterexamples to some conjectures of J. Birman and R. F. Williams concerning the knotting and linking of closed orbits of flows on 3-manifolds. By establishing the existence of ``universal templates,'' we produce examples of flows on containing closed orbits of all knot and link types simultaneously. In particular, the set of closed orbits of any flow transverse to a fibration of the complement of the figure-eight knot in over contains representatives of every (tame) knot and link isotopy class. Our methods involve semiflows on branched 2-manifolds, or *templates*.

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Additional Information

**Robert W. Ghrist**

Affiliation:
Center for Applied Mathematics, Cornell University, Ithaca NY, 14853

Address at time of publication:
Program in Applied and Computational Mathematics, Princeton University, Princeton NJ, 08544-1000; Institute for Advanced Study, Princeton NJ, 08540

Email:
rwghrist@math.princeton.edu; robg@math.ias.edu

DOI:
http://dx.doi.org/10.1090/S1079-6762-95-02006-3

Keywords:
Knots,
links,
branched 2-manifolds,
flows.

Received by editor(s):
June 16, 1995

Additional Notes:
The author was supported in part by an NSF Graduate Research Fellowship.

The author wishes to thank Philip Holmes for his encouragement and support.

Article copyright:
© Copyright 1995
American Mathematical Society