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Local signature of fibered complex surfaces via moduli and monodromy

Ashikaga T.

Demonstratio Mathematica

2010

Vol. 43, nr 2

263-276

The signature of fibered complex surfaces is sometimes localized at finite fiber germs. We analyze this phenomenon by using datum of local monodromy in the mapping class group and a certain rational divisor on the moduli space of stable curves.

Effective dislocation lines in continuously dislocated crystals. I. Material anholonomity

Trzęsowski A.

Journal of Technical Physics

2007

Vol. 48, no 3-4

193-214

A continuous geometric description of Bravais monocrystals with many dislocations and secondary point defects created by the distribution of these dislocations is proposed. Namely, it is distinguished, basing oneself on Kondo and Kröner's Gedanken Experiments for dislocated bodies, an anholonomic triad of linearly independent vector fields. The triad defines local crystallographic directions of the defective crystal as well as a continuous counterpart of the Burgers vector for single dislocations. Next, the influence of secondary point defects on the distribution of many dislocations is modeled by treating these local crystallographic directions, as well as Burgers circuits, as those located in such a Riemannian material space that becomes an Euclidean 3-manifold when dislocations are absent. Some consequences of this approach are discussed.