Combinatorial Cobordism Theory
Abstract
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or topological structure is assumed. This is achieved via a discrete notion of cobordism for which a composition operation is defined. Our main theorem enables the composition of cobordisms by showing that certain sequences of maps between cell complexes are in bijective correspondence with a cell complex of dimension one higher. As a result we obtain a category whose morphisms are cobordisms having a causal structure generalizing that of Causal Dynamical Triangulations as well as dualities inherited from the duality map defined on cell complexes.
Cite
@article{arxiv.2202.13722,
title = {Combinatorial Cobordism Theory},
author = {Maxime Savoy},
journal= {arXiv preprint arXiv:2202.13722},
year = {2022}
}
Comments
83 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:2201.12846