Regularity of line defects in 3-dimensional media

By K. Jänich and Markus Rost (8 pages)

Jänich, Klaus; Rost, Markus. Regularity of line defects in 3-dimensional media. Topology 24 (1985), no. 3, 353-60.

MR 815485, Zbl 588.55012.

Related:

• Jänich, Klaus. Linienfelder mit Verzweigungsdefekten. Regensburger Mathematische Schriften 8. Universität Regensburg, Fachbereich Mathematik, Regensburg, 1984. 41 pp. MR 758079, Zbl 0588.55013.
• Jänich, Klaus. Line fields with branch defects. Manuscripta Math. 48 (1984), no. 1-3, 297-300. MR 753736, Zbl 0588.55014.
• Bechtluft-Sachs, Stefan; Hien, Marco. The global defect index. Comm. Math. Phys. 202 (1999), no. 2, 403-409. MR 1690042, Zbl 1026.55019.

Abbildungsdefekte in 4-Mannigfaltigkeiten

[Mapping defects in 4-manifolds]

by Markus Rost (140 pages)

Dissertation

Regensburger Mathematische Schriften 12, Universität Regensburg, Fachbereich Mathematik, Regensburg, 1987.

MR 893817, Zbl 635.55021.

The thesis constructs for a topological space V its "defect complex DV". The homotopy classes of maps to DV are the homotopy classes of "regularly defect maps" to V. Then special emphasis lies on the computation of the third homotopy group π₃(DV) for some specific V, for instance the Poincaré sphere.

The second homotopy group π₂(DV) appeared as "regularly defect second homotopy group" in Regularity of line defects in 3-dimensional media.

The defect complex DV is described in both references here:

References:

1. Riegel, Ulrich. Bordism of branched line bundles. Math. Nachr. 248/249 (2003), 158-167. MR 1950723, Zbl 1019.57016.
2. Bechtluft-Sachs, Stefan; Riegel, Ulrich; Sixt, Jörg. Bordism of regularly defective maps. Math. Z. 245 (2003), no. 3, 529-543. MR 2021569, Zbl 1058.57026.

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