The Mathematical Institute, University of Oxford, Eprints Archive

Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy

Majumdar, A. and Robbins, J M and Zyskin, M (2009) Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy. Not specified . (Submitted)

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Abstract

Let O be a closed geodesic polygon in S2 . Maps from O into S 2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2 , we evaluate the infimum Dirichlet energy, E(H), for continuous tangent maps of arbitrary homotopy type H. The expression for E(H) involves a topological invariant – the spelling length – associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1(S 2 −{s1 , . . . , sn },∗). These results have applications for the theoretical modelling of nematic liquid crystal devices.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:825
Deposited By:Dr M. Stoll
Deposited On:25 Sep 2009 07:52
Last Modified:25 Sep 2009 07:52

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