Über Erweiterungen von Z und Z2 * Z2 durch nichteuklidische kristallographische Gruppen.
As shown by V. Vassilyev [V], singularities of arbitrary Lagrangian mappings of three-folds form no integral characteristic class. We show, nevertheless, that in the pseudooptical case the number of singularities counted with proper signs forms an invariant. We give a topological interpretation of this invariant, and its applications. The results of the paper may be considered as a 3-dimensional generalization of the results due to V. I. Arnold [A].
For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of...
In each manifold modeled on a finite or infinite dimensional cube , , we construct a meager -subset which is universal meager in the sense that for each meager subset there is a homeomorphism such that . We also prove that any two universal meager -sets in are ambiently homeomorphic.
All maps of type (m,n) are covered by a universal map M(m,n) which lies on one of the three simply connected Riemann surfaces; in fact M(m,n) covers all maps of type (r,s) where r|m and s|n. In this paper we construct a tessellation M which is universal for all maps on all surfaces. We also consider the tessellation M(8,3) which covers all triangular maps. This coincides with the well-known Farey tessellation and we find many connections between M(8,3) and M.