3 citations · 6 across the 6 of their papers we have counts for
7 papers
A note on a local combinatorial formula for the Euler class of a PL spherical fiber bundle
Nikolai Mnëv
We present a local combinatorial formula for the Euler class of a -dimen\-si\-onal PL spherical fiber bundle as a rational number associated to a chain of abs…
Minimal triangulations of circle bundles, circular permutations and binary Chern cocycle
Nikolai Mnëv
We investigate a PL topology question: which circle bundles can be triangulated over a given triangulation of the base? The question got a simple answer emphasizing the role of min…
Which circle bundles can be triangulated over ?
N. Mnëv
We proof that having boundary of standard 3-dimensional simplex as a base of triangulation one can triangulate only trivial and Hopf circle bundles.
A local combinatorial formula for the Chern class of a triangulated bundle in terms of shellings
Nikolai Mnev
Here we are fixing an output of a trivial calculation based on Konsevich's differential 2-form for the Chern class of polygon bundle. As a result an interesting combinatorics and a…
On D.K. Biss' papers "The homotopy type of the matroid Grassmannian" and "Oriented matroids, complex manifolds, and a combinatorial model for BU"
N. Mnev
We point out a flaw in papers by Daniel Biss devoted to homotopy type of matroid Grassmannians.
Combinatorial fiber bundles and fragmentation of a fiberwise PL-homeomorphism
Nikolai Mnev
With a compact PL manifold X we associate a category T(X). The objects of T(X) are all combinatorial manifolds of type X, and morphisms are combinatorial assemblies. We prove that…
Tangent bundle and Gauss functor of a combinatorial manifold
Nikolai Mnev
Pure combinatorial models for BPL_n and Gauss map of a combinatorial manifold are described.