Some results on ramifications

Gilles Bertrand (1)

1 Université Gustave Eiffel

We investigate ramifications, which are simplicial complexes defined by a very simple inductive property: if two complexes X and Y are ramifications, then the union of X and Y is a ramification whenever the intersection of X and Y is a ramification. We show that the collection of all ramifications properly contains the collection of all collapsible complexes, and that it is properly contained in the collection of all contractible complexes. We introduce the notion of a ramification pair, which is a couple of complexes satisfying also an inductive property. We establish a strong relation between ramification pairs and ramifications.

Mots clés: Combinatorial topology; ramifications; contractibility; collapse; completions

Domaines: Mathématique discrète [cs.DM]

Gilles Bertrand. Some results on ramifications. [Research Report] Univ Gustave Eiffel. 2022. ⟨hal-03638665⟩