Global cross sections and minimal flows
This interesting work studies the fine structure of flows with a global cross section that is a closed disk. It is assumed that the first return map is a cellular map, which is here defined as a map bijective on the ambient space, continuous on open cells, and such that the image of any open cell is an open cell. Mind that it is not generally continuous. Geometrically important is the induced branched manifold, essentially a cross section with the one-sided trace of its boundary. It is contractible if and only if the flow lives on a homotopy sphere. Elaborate examples are constructed in dimension 3.
scientific article; zbMATH DE number 1787536