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Topological insights from the Chinese Rings
Author(s):
Józef
H.
Przytycki;
Adam
S.
Sikora
Journal:
Proc. Amer. Math. Soc.
130
(2002),
893-902.
MSC (1991):
Primary 57M25;
Secondary 05C10
Posted:
September 6, 2001
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Abstract:
L. Kauffman conjectured that a particular solution of the Chinese Rings puzzle is the simplest possible. We prove his conjecture by using low-dimensional topology and group theory. We notice also a surprising connection between the Chinese Rings and Habiro moves (related to Vassiliev invariants).
References:
-
- [BC]
- W.W. Rouse Ball and H.S.M. Coxeter, Mathematical Recreations and Essays, University of Toronto Press, Toronto, 1974 (First edition - 1892). MR 50:4229
- [BL]
- J. S. Birman, X. L. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993), 225-270. MR 94d:57010
- [H]
- K. Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000), 1-83, http://www.maths.warwick.ac.uk/gt/GTVol4/paper1.abs.html CMP 2000:07
- [K1]
- L. H. Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990), no. 2, 417-471. MR 90g:57007
- [K2]
- L. H. Kauffman, Tangle complexity and the topology of the Chinese rings, in Mathematical approaches to biomolecular structure and dynamics, IMA Vol. 82, Springer, New York, 1996, 1-10. MR 98b:57013
- [P]
- J. H. Przytycki, Fundamentals of Kauffman bracket skein modules, Kobe J. Math., 16(1), 1999, 45-66, http://xxx.lanl.gov/abs/math. GT/9809113 MR 2000i:57015
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Additional Information:
Józef
H.
Przytycki
Affiliation:
Department of Mathematics, The George Washington University, Washington, DC 20052
Address at time of publication:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
przytyck@gwu.edu
Adam
S.
Sikora
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
asikora@math.umd.edu
DOI:
10.1090/S0002-9939-01-06093-2
PII:
S 0002-9939(01)06093-2
Keywords:
Chinese Rings,
puzzle,
Habiro move
Received by editor(s):
September 10, 1999
Received by editor(s) in revised form:
August 11, 2000
Posted:
September 6, 2001
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2001,
American Mathematical Society
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