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Energy and Thickness of Knots*

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Topology and Geometry in Polymer Science

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 103))

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Abstract

Knots in real physical systems, be they rope or DNA loops, have real physical properties; that is a truism. The behavior of physical knots depends on the topological types of the knots; that is an experimental observation. Mathematical differences between knot types and, more generally, the whole body of knot theory should help explain the physical behavior; that is a hope. If we make the three simplest knots out of similar “rope” having the same lengths Figure 1, we see that one kind of knot seems more “tight” or “compact” than another. Somehow this difference will manifest itself in physical systems and should be predictable from the topology.

The author is supported in part by NSF Grant #DMS9407132.

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  1. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Jonathan Simon

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  1. Jonathan Simon
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Editors and Affiliations

  1. Department of Chemistry, University of Toronto, Toronto, ON, M5S 1A1, Canada

    Stuart G. Whittington

  2. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    Witt De Sumners

  3. Department of Chemistry, University of Minnesota, Minneapolis, MN, 55455, USA

    Timothy Lodge

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Simon, J. (1998). Energy and Thickness of Knots* . In: Whittington, S.G., De Sumners, W., Lodge, T. (eds) Topology and Geometry in Polymer Science. The IMA Volumes in Mathematics and its Applications, vol 103. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1712-1_6

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  • DOI: https://doi.org/10.1007/978-1-4612-1712-1_6

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