Homotopy types of one-dimensional Peano continua
Volume 209 / 2010
Fundamenta Mathematicae 209 (2010), 27-42
MSC: Primary 55P10, 55P15; Secondary 55Q20, 55Q70, 54E45, 20F34.
DOI: 10.4064/fm209-1-3
Abstract
Let $X$ and $Y$ be one-dimensional Peano continua. If the fundamental groups of $X$ and $Y$ are isomorphic, then $X$ and $Y$ are homotopy equivalent. Every homomorphism from the fundamental group of $X$ to that of $Y$ is a composition of a homomorphism induced from a continuous map and a base point change isomorphism.
