Abstract
We give new tools for homotopy Brouwer theory. In particular, we describe a canonical reducing set called the set ofwalls, which splits the plane intomaximal translation areasandirreducible areas. We then focus on Brouwer mapping classes relative to four orbits and describe them explicitly by adding atangleto Handel’s diagram and to the set of walls. This is essentially an isotopy class of simple closed curves in the cylinder minus two points.
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