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Flows on  supporting all links as orbits
Author(s):
Robert
W.
Ghrist
Journal:
Electron. Res. Announc. Amer. Math. Soc.
1
(1995),
91-97.
MSC (1991):
Primary 57M25, 58F22;
Secondary 58F25, 34C35
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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.
References:
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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:
10.1090/S1079-6762-95-02006-3
PII:
S 1079-6762(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.
Communicated by:
Krystyna Kuperberg
Copyright of article:
Copyright
1995,
American Mathematical Society
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