Majumdar, A. and Robbins, J M and Zyskin, M (2009) Tangent unitvector fields: nonabelian homotopy invariants and the Dirichlet energy. Not specified . (Submitted)
This is the latest version of this item.

PDF
209kB 
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 ntimes punctured twosphere, 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 06:52 
Last Modified:  29 May 2015 18:31 
Available Versions of this Item

Tangent unitvector fields: nonabelian
homotopy invariants and the Dirichlet energy. (deposited 24 Sep 2009 12:36) Tangent unitvector fields: nonabelian homotopy invariants and the Dirichlet energy. (deposited 25 Sep 2009 06:52) [Currently Displayed]
Repository Staff Only: item control page