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Umbilical characteristic number of Lagrangian mappings of 3-dimensional pseudooptical manifolds

Maxim È. Kazarian (1996)

Banach Center Publications

As shown by V. Vassilyev [V], D 4 ± singularities of arbitrary Lagrangian mappings of three-folds form no integral characteristic class. We show, nevertheless, that in the pseudooptical case the number of D 4 ± 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].

Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion

Anna Beliakova, Christian Blanchet, Thang T. Q. Lê (2008)

Fundamenta Mathematicae

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...

Universal meager F σ -sets in locally compact manifolds

Taras O. Banakh, Dušan Repovš (2013)

Commentationes Mathematicae Universitatis Carolinae

In each manifold M modeled on a finite or infinite dimensional cube [ 0 , 1 ] n , n ω , we construct a meager F σ -subset X M which is universal meager in the sense that for each meager subset A M there is a homeomorphism h : M M such that h ( A ) X . We also prove that any two universal meager F σ -sets in M are ambiently homeomorphic.

Universal tessellations.

David Singerman (1988)

Revista Matemática de la Universidad Complutense de Madrid

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.

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