Some aspects of the theory of defects of ordered media and gauge fields related to foliations

DOI10.1007/BF01213598zbMath0485.58018MaRDI QIDQ1164303

Valentin Poénaru

Publication date: 1981

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

classifying spacesgauge theorydefect of two dimensional smecticshomotopy theory of defects of ordered mediaisolated singularities of a line field of the planemanifolds of internal statesobstructions to extend a foliation through a singular locussingularities of measured foliations

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Applications of dynamical systems (37N99) Fredholm structures on infinite-dimensional manifolds (58B15) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Foliations in differential topology; geometric theory (57R30) Homotopy groups (55Q99)

Related Items (6)

An SBV relaxation of the cross-Newell energy for modeling stripe patterns and their defects ⋮ Use of meanders and train tracks for description of defects and textures in liquid crystals and \(2+1\) gravity ⋮ Use of quadratic differentials for description of defects and textures in liquid crystals and \(2+1\) gravity ⋮ Aspects of defect topology in smectic liquid crystals ⋮ Topology in Liquid Crystal Phases ⋮ Computing with non-orientable defects: nematics, smectics and natural patterns

Cites Work

• Differential forms. With applications to the physical sciences
• Integral Formalism for Gauge Fields
• Morse Theory. (AM-51)
• Topological solitons and graded Lie algebras
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