Related papers: The Borsuk-Ulam theorem for closed 3-dimensional m…

Let $M$ be a closed 3-manifold which admits the geometry $S^2\times \R$. In this work we determine all the free involutions $\tau$ on $M$, and the Borsuk-Ulam index of $(M,\tau)$.

Let M be a Seifert manifold which belongs to the geometry Flat. In this work we determine all the free involutions {\tau} on M, and the Borsuk-Ulam indice of (M,{\tau}).

We study the Borsuk-Ulam theorem for triple (M;\tau; \R^n), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution \tau. The largest value of n for which the Borsuk-Ulam theorem holds is called the Z_2-index…

For each sapphire Sol $3$-manifold, we classify the free involutions. For each triple $(M, \tau; R^n)$ where $M$ is a sapphire Sol $3$-manifold and $\tau$ is a free involution, we show if $(M, \tau; R^n)$ has the Borsuk-Ulam property or…

This paper establishes a Borsuk-Ulam type theorem for PL-manifolds with a finite group action, depending on the free equivariant cobordism class of a manifold. In particular, necessary and sufficient conditions are considered for a manifold…

Let M and N be topological spaces such that M admits a free involution $\\tau$. A homotopy class $\beta$ $\in$ [M, N ] is said to have the Borsuk-Ulam property with respect to $\\tau$ if for every representative map f : M $\rightarrow$ N of…

The moduli space of planar polygons with generic side lengths is a closed, smooth manifold. Mapping a polygon to its reflected image across the $X$-axis defines a fixed-point-free involution on these moduli spaces, making them into free…

We observe that the classical Borsuk-Ulam theorem has an easy generalization to maps from an n-manifold M^n to R^n. We point out a geometric corollary.

Let (X, t, S) be a triple, where S is a compact, connected surface without boundary, and t is a free cellular involution on a CW-complex X. The triple (X, t, S) is said to satisfy the Borsuk-Ulam property if for every continuous map…

Let $M$ and $N$ be fiber bundles over the same base $B$, where $M$ is endowed with a free involution $\tau$ over $B$. A homotopy class $\delta \in [M,N]_{B}$ (over $B$) is said to have the Borsuk-Ulam property with respect to $\tau$ if for…

In this work we analysed the validity of a type of Borsuk-Ulam theorem for multimaps between surfaces. We developed an algebraic technique involving braid groups to study this problem for $n$-valued maps. As a first application we described…

The purpose of this work is to classify, for given integers $m,\, n\geq 1$, the bordism class of a closed smooth $m$-manifold $X$ with a free smooth involution $\tau$ with respect to the validity of the {\it Borsuk-Ulam property} that for…

We consider spaces with free involutions that satisfy the Borsuk - Ulam theorems (BUT-spaces). There are several equivalent definitions for BUT-spaces that can be considered as their properties. Our main technical tool is Yang's…

Let $M$ be a topological space that admits a free involution $\tau$, and let $N$ be a topological space. A homotopy class $\beta \in [ M,N ]$ is said to have the Borsuk-Ulam property with respect to $\tau$ if for every representative map…

For finite connected graphs $\Gamma$ and $G$, with $\Gamma$ admitting a free involution $\tau$, we characterize the based homotopy classes $\alpha\in[\Gamma,G]$ for which the Borsuk-Ulam property holds in the sense of Gon\c{c}alves, Guaschi…

In this paper we present a Kakutani type theorem that is equivalent to the Borsuk--Ulam theorem for manifolds.

A generalization of the Borsuk-Ulam theorem to Stiefel manifolds is considered. This theorem is applied to derive bounds on $d$ that guarantee-for a given set of $m$ measures in $\mathbb{R}^d$-the existence of $k$ mutually orthogonal…

Let $M$ be a topological space that admits a free involution $\tau$, and let $N$ be a topological space. A homotopy class $\beta \in [ M,N ]$ is said to have {\it the Borsuk-Ulam property with respect to $\tau$} if for every representative…

We study Borsuk-Ulam type results for the loopspace of an euclidean sphere without loops equal to their inverses.

We compute the Nielsen-Borsuk-Ulam number for any selfmap of $n-$torus, $\mathbb{T}^n$, as well as any free involution $\tau$ in $\mathbb{T}^n$, with $n \leqslant 3$. Finally, we conclude that the tori, $\mathbb{T}^1$, $\mathbb{T}^2$ and…