  Topological connections in the single-streaming voids and multistreaming
filaments and walls reveal a cosmic web structure different from traditional
mass density fields. A single void structure not only percolates the
multistream field in all the directions, but also occupies over 99 per cent of
all the single-streaming regions. Sub-grid analyses on scales smaller than
simulation resolution reveal tiny pockets of voids that are isolated by
membranes of the structure. For the multistreaming excursion sets, the
percolating structure is significantly thinner than the filaments in
over-density excursion approach.
  Hessian eigenvalues of the multistream field are used as local geometrical
indicators of dark matter structures. Single-streaming regions have most of the
zero eigenvalues. Parameter-free conditions on the eigenvalues in the
multistream region may be used to delineate primitive geometries with
concavities corresponding to filaments, walls and haloes.
