title: Deforestation of Peano continua and minimal deformation retracts.
abstract: Every Peano continuum has a strong deformation retract to adeforestedcontinuum, that is, one with no strongly contractible subsets attached at a single point. In a deforested continuum, each point with a one-dimensional neighborhood is either fixed by every self-homotopy of the space, or has a neighborhood which is a locally finite graph. A minimal deformation retract of a continuum (if it exists) is called itscore. Every one-dimensional Peano continuum has a unique core, which can be obtained by deforestation. We give examples of planar Peano continua that contain no core but are deforested.
authors.affiliation: Math Department, Brigham Young University, Provo, UT 84602, USA.
authors.forename: G
authors.initials: G
authors.lastname: Conner
authors.forename: M
authors.initials: M
authors.lastname: Meilstrup
keywords: Deformation retract; Homotopy equivalence; One-dimensional; Peano continua; Reduced forms