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 −,∗). These results have applications for the theoretical modelling of nematic liquid crystal devices.

Item Type: | Article |
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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 |

### Available Versions of this Item

- Tangent unit-vector fields: nonabelian

homotopy invariants and the Dirichlet energy. (deposited 24 Sep 2009 13:36)- Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy. (deposited 25 Sep 2009 07:52)
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- Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy. (deposited 25 Sep 2009 07:52)

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