Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy
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 arbitrar...
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| Format: | Journal article |
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2009
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| _version_ | 1797050421808726016 |
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| author | Majumdar, A Robbins, J Zyskin, M |
| author_facet | Majumdar, A Robbins, J Zyskin, M |
| author_sort | Majumdar, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T18:04:54Z |
| format | Journal article |
| id | oxford-uuid:011d7437-583a-4972-917e-88921ce8f23a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:04:54Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:011d7437-583a-4972-917e-88921ce8f23a2022-03-26T08:33:06ZTangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:011d7437-583a-4972-917e-88921ce8f23aMathematical Institute - ePrints2009Majumdar, ARobbins, JZyskin, MLet 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. |
| spellingShingle | Majumdar, A Robbins, J Zyskin, M Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy |
| title | Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy
|
| title_full | Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy
|
| title_fullStr | Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy
|
| title_full_unstemmed | Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy
|
| title_short | Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy
|
| title_sort | tangent unit vector fields nonabelian homotopy invariants and the dirichlet energy |
| work_keys_str_mv | AT majumdara tangentunitvectorfieldsnonabelianhomotopyinvariantsandthedirichletenergy AT robbinsj tangentunitvectorfieldsnonabelianhomotopyinvariantsandthedirichletenergy AT zyskinm tangentunitvectorfieldsnonabelianhomotopyinvariantsandthedirichletenergy |