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Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants

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Lectures on Topological Fluid Mechanics

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1973))

Abstract

Many topological calculations can be done most easily using the basic idea of winding number. This chapter demonstrates the use of winding number techniques in calculating writhe, linking number, twist, and higher order braid invariants. The writhe calculation works for both closed and open curves. These measures have applications in molecular biology, materials science, fluid mechanics and astrophysics.

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Authors and Affiliations

  1. Mathematics Dept., SECAM, University of Exeter, North Park Rd., EX4 4QE, Exeter, U.K.

    Mitchell A. Berger

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  1. Mitchell A. Berger
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Correspondence to Mitchell A. Berger .

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Editors and Affiliations

  1. Dipto. Matematica e Applicazioni, Università Milano-Bicocca, Via R. Cozzi 53, Milano, 20125, Italy

    Renzo L. Ricca

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Berger, M.A. (2009). Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants. In: Ricca, R. (eds) Lectures on Topological Fluid Mechanics. Lecture Notes in Mathematics(), vol 1973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00837-5_2

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