arXiv subjects

Daniel Vendrúscolo

Publications and source records attributed to Daniel Vendrúscolo.

6 recordsLinked to original sources

arXiv2026

A study of $n$-valued non-split maps and applications

For a given $n$-valued map, there exists a suitable minimal covering of the domain such that the composition of this covering with the map yields a split map, composed of $n$ single-valued maps, called the lift factors. Using the group action of the deck-transformation group we construct intermediate covering spaces as well as intermediate configuration spaces, allowing the original map to lift to these spaces, building a tower to illustrate at which level the lift factors split off. We then display two applications of these new tools. The first is to derive results concerning the Borsuk-Ulam property for certain coverings of the tower. The second is to obtain a sharp formula for the Nielsen number of an $n$-valued non-split map, using the coincidence number of specific single-valued maps that arise in the lifts of the tower.

math.AT↗

arXiv2022

The $R_\infty$ property for nilpotent quotients of generalized solvable Baumslag-Solitar groups

We say a group $G$ has property $R_\infty$ if the number $R(φ)$ of twisted conjugacy classes is infinite for every automorphism $φ$ of $G$. For such groups, the $R_\infty$-nilpotency degree is the least integer $c$ such that $G/γ_{c+1}(G)$ has property $R_\infty$. In this work, we compute the $R_\infty$-nilpotency degree of all Generalized Solvable Baumslag-Solitar groups $Γ_n$. Moreover, we compute the lower central series of $Γ_n$, write the nilpotent quotients $Γ_{n,c}=Γ_n/γ_{c+1}(Γ_n)$ as semidirect products of finitely generated abelian groups and classify which integer invertible matrices can be extended to automorphisms of $Γ_{n,c}$.

math.GR↗

arXiv2021

Nielsen-Borsuk-Ulam number for maps between tori

We compute the Nielsen-Borsuk-Ulam number for any selfmap of $n-$torus, $\mathbb{T}^n$, as well as any free involution $τ$ in $\mathbb{T}^n$, with $n \leqslant 3$. Finally, we conclude that the tori, $\mathbb{T}^1$, $\mathbb{T}^2$ and $\mathbb{T}^3$, are Wecken spaces in Nielsen-Borsuk-Ulam theory. Such a number is a lower bound for the minimal number of pair of points such that $f(x)=f(τ(x))$ in a given homotopy class of maps.

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arXiv2014

Involutions on sapphire Sol 3-manifolds and the Borsuk-Ulam theorem for maps into $R^n$

For each sapphire Sol $3$-manifold, we classify the free involutions. For each triple $(M, τ; R^n)$ where $M$ is a sapphire Sol $3$-manifold and $τ$ is a free involution, we show if $(M, τ; R^n)$ has the Borsuk-Ulam property or not. It is known that for $n>3$ the Borsuk-Ulam property does not hold independent of the involution, so we provide a classification when $n=2$ and $3$.

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arXiv2007

Jiang-type theorems for coincidences of maps into homogeneous spaces

Let $f,g: X\to G/K$ be maps from a closed connected orientable manifold $X$ to an orientable coset space $M=G/K$ where $G$ is a compact connected Lie group, $K$ a closed subgroup and $\dim X=\dim M$. In this paper, we show that if $L(f,g)=0$ then $N(f,g)=0$; if $L(f,g)\ne 0$ then $N(f,g)=R(f,g)$ where $L(f,g), N(f,g)$, and $R(f,g)$ denote the Lefschetz, Nielsen, and Reidemeister coincidence numbers of $f$ and $g$, respectively. When $\dim X> \dim M$, we give conditions under which $N(f,g)=0$ implies $f$ and $g$ are deformable to be coincidence free.

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arXiv2004

Coincidence classes in nonorientable manifolds

In this article we studied Nielsen coincidence theory for maps between manifolds of same dimension without hypotheses on orientation. We use the definition of semi-index of a class, we review the definition of defective classes and study the appearance of defective root classes. We proof a semi-index product formula type for lifting maps and we presented conditions such that defective coincidence classes are the only essencial classes.

math.AT↗