Combing Euclidean buildings

Abstract

For an arbitrary Euclidean building we define a certain combing, which satisfies the “fellow traveller property” and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order preserving automorphisms on a Euclidean building of one of the types $A_n,B_n,C_n$ admits a biautomatic structure.