Jänich, K.; Rost, M. Regularity of line defects in 3-dimensional media. (English) Zbl 0588.55012 Topology 24, 353-360 (1985). A boundary value problem in the context of this work essentially is an extension problem of the following type: Given a 3-manifold M, a (defect) map into some parameter space V, defined on ”most” of the boundary \(\partial M\), is to be extended as a (defect) map on M. A ”regularly defect second homotopy group” serves as the coefficient group of a homology obstruction for boundary value problems enjoying certain regularity properties. The parameter space V is defined to have the regular defects property, if all such boundary value problems involving V have a regularly defect solution. Theorem: If \(\Gamma\) \(\subset SO(3)\) is finite then \(V=S0(3)/\Gamma\) has the regular defects property. Investigating the regularly defect second homotopy group shows that the regular defects property depends only on the fundamental group of the parameter space; among other results, a necessary and sufficient condition for this property is found. A final paragraph discusses implications of this work for defects in ordered media in physics. Reviewer: D.Erle Cited in 1 ReviewCited in 1 Document MSC: 55S36 Extension and compression of mappings in algebraic topology 55S40 Sectioning fiber spaces and bundles in algebraic topology 57M12 Low-dimensional topology of special (e.g., branched) coverings 55S35 Obstruction theory in algebraic topology 55Q70 Homotopy groups of special types 74A99 Generalities, axiomatics, foundations of continuum mechanics of solids 57R22 Topology of vector bundles and fiber bundles 57R20 Characteristic classes and numbers in differential topology 57M05 Fundamental group, presentations, free differential calculus Keywords:defect map; boundary value problem; 3-manifold; regularly defect second homotopy group; homology obstruction; regular defects property; regularly defect solution; fundamental group; parameter space; ordered media PDFBibTeX XMLCite \textit{K. Jänich} and \textit{M. Rost}, Topology 24, 353--360 (1985; Zbl 0588.55012) Full Text: DOI