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 |
|---|---|
| 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) [Currently Displayed]
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