arXiv subjects
Publications and source records attributed to C. Hayat.
Let $M$ be a closed 3-manifold which admits the geometry $S^2\times \R$. In this work we determine all the free involutions $τ$ on $M$, and the Borsuk-Ulam index of $(M,τ)$.
Let M be a closed, connected 3-manifold which admits Nil geometry, we determine all free involutions $τ$ on M and the Borsuk-Ulam index of $(M,τ)$.
Let M be a Seifert manifold which belongs to the geometry Flat. In this work we determine all the free involutions τ on M, and the Borsuk-Ulam indice of (M,τ).
It is classical that given any Seifert structure on N, Reidemeister-Schreier's algorithm produces a presentation of all index 2 subgroups of the fundamental group of N, described as the fundamental group of some Seifert manifolds. The new result of this article is concise formulas that gather all possible cases.
The cohomology ring with coefficients in $\Z_p$, where $p$ is a prime integer, of a Seifert manifold $M$, orientable or not orientable is obtained from a simplicial decomposition of $M$. Many choices must be made before applying Alexander-Whitney formula to get the cup-products. The most difficult choices are those of liftings from the cellular complex to the simplicial complex when we add the condition to be cocycles.