Classifying Homotopy Types of One-Dimensional Peano Continua Classifying Homotopy Types of One-Dimensional Peano Continua

by Meilstrup, Mark H

Determining the homotopy type of one-dimensional Peano continua has been an open question of some interest. We give a complete invariant of the homotopy type of such continua, which consists of a pair of subspaces together with a relative homology group. Along the way, we describe reduced forms for one-dimensional Peano continua.