Jeremy Brazas

collaborators

8 papers

math.GN2026

Transfinitely iterated wild sets

Jeremy Brazas, Atish Mitra

In this paper, we study homotopical analogues of the Cantor-Bendixson derivative. For each $n \geq 0$ , the " $I ¨ _{n}$ -wild set" $w_{n} (X)$ of a topological space $X$ is the subs…

math.AT2026

On R-trees, homotopies, and covering maps

Jeremy Brazas, Gregory R. Conner, Paul Fabel +1

A map $p : E \to X$ has the \emph{unique path lifting} property if every path in $X$ , after a choice of an initial point, lifts uniquely to a path in $E$ . We prove that if a group $G$ …

math.GT2026

Tree-like is not a transitive relation on paths

Jeremy Brazas, Gregory R. Conner, Paul Fabel +1

The notions of tree-like loop and Lipschitz tree-like loop were introduced by Hambly and Lyons in their 2010 Annals of Mathematics paper. They showed that the Lipschitz tree-like p…

math.AT2025

Motion Planning on One-Dimensional Peano Continua

Jeremy Brazas, Petar Pavesic

We study the Lusternik-Schnirelmann category and topological complexity of 1-dimensional spaces. We define both invariants as lengths of suitable closed filtrations, as opposed to…

math.AT2025

The Äech homotopy groups of a shrinking wedge of spheres

Jeremy Brazas

We compute the Äech homotopy groups of the $m$ -dimensional infinite earring space $E_{m}$ , i.e. a shrinking wedge of $m$ -spheres. In particular, for all $n, m \geq 2$ , we pro…

math.AT2025

Nonlocal loss of first homotopy in polyhedral approximations of Peano continua

Jeremy Brazas, Hanspeter Fischer

If a Peano continuum $X$ is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of $X$ . In general, this fails…

Transfinitely iterated wild sets

On R-trees, homotopies, and covering maps

Tree-like is not a transitive relation on paths

Motion Planning on One-Dimensional Peano Continua

The Äech homotopy groups of a shrinking wedge of spheres

Nonlocal loss of first homotopy in polyhedral approximations of Peano continua

The Äech homotopy groups of a shrinking wedge of spheres