Combinatorial Cell Complexes: Duality, reconstruction and causal cobordisms

Understand

This thesis proposes a framework based on a notion of combinatorial cell complex (cc) whose cells are defined simply as finite sets of vertices.

• The cells of a cc are subject to four axioms involving a rank function that assigns a rank (or a dimension) to each cell.
• Our framework focuses on classes of cc admitting an inclusion-reversing duality map.
• We introduce a combinatorial notion of cobordism that allows us to single out a category whose morphisms are cobordisms having a causal structure.