Searcharxiv⌕ Search

arXiv subjects

F. González-Acuña

Publications and source records attributed to F. González-Acuña.

7 recordsLinked to original sources
arXiv2018

$2$-stratifolds with fundamental group $\mathbb{Z}$

$2$-stratifolds are a generalization of $2$-manifolds that occur as objects in applications such as in TDA. These spaces can be described by an associated bicoloured labelled graph. In previous papers we obtained a classification of 1-connected trivalent $2$-stratifolds. In this paper we classify trivalent $2$-stratifolds that have fundamental group $\mathbb{Z}$. This classification implicitly gives an efficient algorithm that applies to a bicoloured labelled graph to decide wether the associated $2$-stratifold has fundamental group $\mathbb{Z}$.

math.GT↗
arXiv2018

Models of Simply-connected Trivalent $2$-dimensional Stratifolds with an Implementation Code

Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We develop operations on their associated labeled graphs that will effectively construct from a single vertex all graphs that represent $1$-connected $2$-stratifolds. We describe an implementation on Python of these operations and other previous results.

math.GT↗
arXiv2017

2-stratifold spines of closed 3-manifolds

$2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed branch curves. We obtain a list of all closed $3$-manifolds that have a $2$-stratifold as a spine.

math.GT↗
arXiv2017

$2$-stratifold groups have solvable Word Problem

$2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where several sheets meet. We show that the word problem for fundamental groups of $2$-stratifolds is solvable.

math.GT↗
arXiv2016

Classification and Models of Simply-connected Trivalent $2$-dimensional Stratifolds

Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We obtain a classification of $1$-connected $2$-stratifolds in terms of their associated labeled graphs and develop operations that will construct from a single vertex all graphs that represent $1$-connected $2$-stratifolds.

math.GT↗
arXiv2015

2-dimensional stratifolds

2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data analysis. We define 2-stratifolds and study properties of their associated labeled graphs that determine which ones are simply connected.

math.GT↗