On the geometry on the nondegenerate subspaces of orthogonal space

Source abstract

The present article is part of the program described in Bennett, R. Gramlich, C. Hoffman, S. Shpectorov. Here we study the Phan-theoretic flipflop geometries related to the flip induced by a nondegenerate orthogonal form on a vector space over an arbitrary field of characteristic distinct from two. We obtain amalgam results in the spirit of Phan's theorems for fields that do not admit a quadratic extension and for real closed fields.