On isometries of twin buildings (Q2028013)

The authors consider thick \(2\)-spherical twin buildings and prove that every isometry between augmented foundations of two such buildings has a suitable extension. This is motivated by the aim to obtain a local-to-global result (saying that the local structure determines the whole building) without using the additional condition (co) as in [the third author and \textit{M. Ronan}, Invent. Math. 122, No. 1, 71--81 (1995; Zbl 0854.51009)]. The authors announce that the local-to-global result will be proved for all affine twin buildings of rank at least \(3\) in a subsequent paper.