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Properties of Knot Energies

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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))

Abstract

Energy functions on knots are continuous and scale-invariant functions defined from knot conformations into non-negative real numbers. The infimum of an energy function is an invariant which defines (not necessarily unique) “canonical conformations” of knots in three space. Many (infinite) hierarchies of energy functions for knots in the mathematical and physical science literature have been studied, each energy function with its own (characteristic) set of properties. In this paper we examine energy functions, and classify them as either basic, strong, charge or tight,depending on the properties of the energies for different knot conformations. Knot invariants derived from these energy functions are expected to be useful.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Kennesaw State College, Kennesaw, GA, 30144, USA

    Y. Diao

  2. Department of Mathematics, Western Kentucky University, Bowling Green, KY, 42101, USA

    C. Ernst

  3. Department of Mathematics and Statistics, York University, North York, Ontario, M3J 1P3, Canada

    E. J. Janse van Rensburg

Authors
  1. Y. Diao
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  2. C. Ernst
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  3. E. J. Janse van Rensburg
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Editor information

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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© 1998 Springer-Verlag New York, Inc.

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Diao, Y., Ernst, C., van Rensburg, E.J.J. (1998). Properties of Knot Energies. 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_5

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  • DOI: https://doi.org/10.1007/978-1-4612-1712-1_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98580-0

  • Online ISBN: 978-1-4612-1712-1

  • eBook Packages: Springer Book Archive

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