Acta Applicandae Mathematica

, Volume 8, Issue 1, pp 65–74

Topological properties of ordinary nematics in 3-space

  • Klaus Jänich
Article

Abstract

This paper describes the topologically possible global defect behavior of ordinary nematics in 3-space. It is written for physicists interested in defects of ordered media as well as for topologists, but instead of using an ‘intermediate’ way of presentation, which might appeal to no one, we first state the result for physicists and then, discussing the proof, turn to mathematicians and physicists who are inclined to read a mathematical paper.

AMS (MOS) subject classifications (1980)

82A99 57R25 57M25 

Key words

Defects in ordered media nematic liquids linking numbers Poincaré-Hopf theorems 

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References

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    Jänich, K. and Trebin, H.-R.: ‘Disentanglement of Line Defects in Ordered Media’, in R. Balian et al. (eds.), Les Houches, Session XXXV, 1980—Physics of Defects, North-Holland Publishing Company, 1981, pp. 421–429.Google Scholar
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    Olum, P.: ‘Obstructions to Extensions and Homotopies’, Ann. Math. 52 (1950), 1–50.Google Scholar
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    Olum, P.: ‘On Mappings into Spaces in which Certain Homotopy Groups Vanish’, Ann. Math. 57 (1953), 561–574.Google Scholar
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    Poénaru, V. and Toulouse, G.: ‘The Crossing of Defects in Ordered Media and the Topology of 3-manifolds’, J. Phys. 38 (1977) 887–895.Google Scholar
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    Rolfson, D.: Knots and Links, Publish or Perish, Berkeley, 1976.Google Scholar

Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Klaus Jänich
    • 1
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgWest Germany

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