Javier Mart'inez

collaborators

3 papers

math.GT2025

Affine representations of rational and pretzel knots

Javier Martínez

We construct and study representations of rational and pretzel tangle and knot groups into the affine group $AGL (1, C)$ , via a TQFT that is valued in the category…

math.GT2025

Representations of knot groups in $AGL_{1} (C)$ and Alexander invariants

Ángel González-Prieto, Javier Martínez, Vicente Muñoz

This paper reinterprets Alexander-type invariants of knots via representation varieties of knot groups into the group $AGL_{1} (C)$ of affine transformations of the…

math.GN2019

The hyperspaces $H S (p, X)$

Florencio Corona-Vázquez, Russell Aarón Quiñones-Estrella, Javier Sánchez Martínez

Let $X$ be a continuum and let $C (X)$ denote the hyperspace of subcontinua of $X$ , endowed with the Hausdorff metric. For $p \in X$ , define the hyperspace $C(p,X)=\{A\in C(X):p\in A…

Affine representations of rational and pretzel knots

Representations of knot groups in AGL1​(C) and Alexander invariants

The hyperspaces HS(p,X)

Representations of knot groups in $AGL_{1} (C)$ and Alexander invariants

The hyperspaces $H S (p, X)$