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Subspaces of knot spaces

Author(s): Craig Benham; Xiao-Song Lin; David Miller
Journal: Proc. Amer. Math. Soc. 129 (2001), 3121-3127.
MSC (1991): Primary 57M25, 53A04; Secondary 92B05
Posted: March 29, 2001
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Abstract:

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.

References:

[BM]
C. Benham and D. Miller, Fixed-writhe isotopies and the topological conservation law for closed, circular DNA, Journal of Knot theory and its Ramifications, 5 (1996), 859-866. MR 98b:57019

[F1]
F.B. Fuller, Decomposition of the linking number of a closed ribbon: A problem from molecular biology, Proc. Natl. Acad. Sci. USA, 75 (1978), 3557-3561. MR 58:9367

[F2]
F.B. Fuller, The writhing number of a Space Curve, Proc. Natl. Acad. Sci. USA, 68 (1971), 815-819. MR 43:3928

[GP]
H. Gluck and L.H. Pan, Knot theory in the presence of curvature I, University of Pennsylvania preprint, 1994.

[H1]
A. Hatcher, A proof of the Smale conjecture, Ann. of Math. 117 (1983), 553-607. MR 85c:57008

[H2]
A. Hatcher, Spaces of Knots, Cornell University Preprint, 1999, http://www.math.cornell.edu/ $^{\symbol{126}}$hatcher.

[P]
W.F. Pohl, the self-linking number of a closed space curve, Journal of Mathematics and Mechanics, 17 (1968), 975-985. MR 36:5827

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Additional Information:

Craig Benham
Affiliation: Department of Biomathematical Sciences, Mount Sinai School of Medicine, One Gustave Levy Place, New York, New York 10029
Email: BENHAM@msvax.mssm.edu

Xiao-Song Lin
Affiliation: Department of Mathematics, University of California Riverside, Riverside, California 92521
Email: xl@math.ucr.edu

David Miller
Affiliation: Department of Mathematics, William Paterson University, Wayne, New Jersey 07470
Email: damiller@pilot.njin.net

DOI: 10.1090/S0002-9939-01-05913-5
PII: S 0002-9939(01)05913-5
Keywords: Knots, writhe, DNA topology, knot spaces
Received by editor(s): June 28, 1999
Received by editor(s) in revised form: March 6, 2000
Posted: March 29, 2001
Additional Notes: The first author was supported in part by NIH Grant RO1-GM47012
The second author was supported in part by NSF Grant DMS-9704726
The third author was supported in part by NSF Grant DMS-9732675
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2001, American Mathematical Society

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