Reconstruction of infinite matroids from their 3-connected minors
  We show that any infinite matroid can be reconstructed from the torsos of a tree-decomposition over its 2-separations, together with local information at the ends of the tree. We show that if the matroid is tame then this local information is simply a choice of whether circuits are permitted to use that end. The same is true if each torso is planar, with all gluing elements on a common face. 
Nathan Bowler, Johannes Carmesin, Luke Postle
math.CO