In this paper we define a Poincaré-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial “torsion-type” invariant which refines the PR-metric introduced in [Fa] and contains an additional sign or phase information. We compute the PR-scalar product in terms of the torsions of Euler ...

I Koizumi, op. cit., 2, 267. 10 0. Zariski, "The Reduction of the Singularities of an Algebraic Surface," Ann. Math., 40, 639689, 1939; "A Simplified Proof for the Resolution of Singularities of an Algebraic Surface," ibid., 43, 583-593, 1942; S. Abhyankar, "The Theorem of Local Uniformization on Algebraic Surfaces over Modular Fields," Ann. Math. (to appear). "0. Zariski, "Pencils on an Algebr...

Abstract We prove that the Stiefel–Whitney classes of a moment-angle manifold, not necessarily smooth, are trivial. also consider partial quotient manifold.

We determine a nice simple formula for the largest Euclidean space which there is an orientable n -manifold with nonimmersion detected by Stiefel-Whitney classes. For Spin manifolds, we prove analogue of upper bound and establish complete answer ≤ 23 32 33 . Results similar to many these were obtained some 50 years ago, but in much less tractable form. The sharp results manifolds require detail...

A quasi-regular cell complex is defined and shown to have a reasonable barycentric subdivision. In this setting, Whitney's theorem that the ^-skeleton of the barycentric subdivision of a triangulated n-manifold is dual to the (n /c)th Stiefel-Whitney cohomology class is proven, and applied to projective spaces, lens spaces and surfaces. 1. QR complexes. A (finite) cell structure on a space X is...