Subspaces of knot spaces
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- by Craig Benham, Xiao-Song Lin and David Miller PDF
- Proc. Amer. Math. Soc. 129 (2001), 3121-3127 Request permission
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
- David Miller and Craig Benham, Fixed-writhe isotopies and the topological conservation law for closed, circular DNA, J. Knot Theory Ramifications 5 (1996), no. 6, 859–866. MR 1422129, DOI 10.1142/S0218216596000461
- F. Brock Fuller, Decomposition of the linking number of a closed ribbon: a problem from molecular biology, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 8, 3557–3561. MR 490004, DOI 10.1073/pnas.75.8.3557
- F. Brock Fuller, The writhing number of a space curve, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 815–819. MR 278197, DOI 10.1073/pnas.68.4.815
- H. Gluck and L.H. Pan, Knot theory in the presence of curvature I, University of Pennsylvania preprint, 1994.
- Allen E. Hatcher, A proof of the Smale conjecture, $\textrm {Diff}(S^{3})\simeq \textrm {O}(4)$, Ann. of Math. (2) 117 (1983), no. 3, 553–607. MR 701256, DOI 10.2307/2007035
- A. Hatcher, Spaces of Knots, Cornell University Preprint, 1999, http://www.math.cornell.edu/~hatcher.
- William F. Pohl, The self-linking number of a closed space curve, J. Math. Mech. 17 (1967/1968), 975–985. MR 0222777
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
- Received by editor(s): June 28, 1999
- Received by editor(s) in revised form: March 6, 2000
- Published electronically: 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 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3121-3127
- MSC (1991): Primary 57M25, 53A04; Secondary 92B05
- DOI: https://doi.org/10.1090/S0002-9939-01-05913-5
- MathSciNet review: 1840119