Collapses and watersheds in pseudomanifolds Collapses and watersheds in pseudomanifolds

Jean Cousty, Gilles Bertrand, Michel Couprie, Laurent Najman, Jean Cousty, Gilles Bertrand, Michel Couprie, Laurent, Jean Cousty, Gilles Bertrand, Michel Couprie, Laurent Najman
2009 unpublished
This work is settled in the framework of abstract simplicial complexes. We propose a definition of a watershed and of a collapse for maps defined on pseudomanifolds of arbitrary dimension. Through an equivalence theorem, we establish a deep link between these two notions: any watershed can be obtained by collapse iterated until idempotence, and conversely any collapse iterated until idempotence induces a watershed. We also state an equivalence result which links the notions of a watershed and
more » ... a collapse with the one of a minimum spanning forest.
fatcat:inn4w4ae4nendnfd3gwfymoaui