TY - JOUR
T1 - Tangent unit-vector fields
T2 - nonabelian homotopy invariants and the Dirichlet energy
AU - Majumdar, Apala
AU - Robbins, J. M.
AU - Zyskin, Maxim
PY - 2009/10
Y1 - 2009/10
N2 - Let O be a closed geodesic polygon in S2. Maps from O into S2 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(S2−{s1,…,sn},∗). These results have applications for the theoretical modelling of nematic liquid crystal devices.
AB - Let O be a closed geodesic polygon in S2. Maps from O into S2 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(S2−{s1,…,sn},∗). These results have applications for the theoretical modelling of nematic liquid crystal devices.
UR - http://dx.doi.org/10.1016/j.crma.2009.09.002
U2 - 10.1016/j.crma.2009.09.002
DO - 10.1016/j.crma.2009.09.002
M3 - Article
SN - 1631-073X
VL - 347
SP - 1159
EP - 1164
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 19-20
ER -