Colloquium

Buildings and the Moufang Property

by Richard Weiss, Professor ofMathematics, Tufts University, Medford, Massachusetts

Abstract

In his famous Lecture Notes of 1974, Jacques Titsgave a classification of (thick irreducible)spherical buildings of rank at leastthree. He observed in the addenda to that workthat every residue (the most importantclass of subbuildings) of rank at least two of such a buildinghas a symmetry property he called the Moufang condition (in honorof Ruth Moufang's work in the early 1930's on projective planes)and proposed the two projects of classifying (thick irreducible)spherical buildings of rank two (equivalently, generalizedpolygons) which satisfy the Moufang condition and using such a classificationto reprove the classification of spherical buildings of rankgreater than two. In joint work with Tits, these two projectshave now been completed. We will give a brief overviewof this work.