Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic

Karl Auinger; Mikhail Volkov

Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic

Category Theory 2026-03-18 v2 Group Theory Geometric Topology

Authors: Karl Auinger , Mikhail Volkov

Abstract

We introduce a complete set of combinatorial data that encode the category $2\mathfrak{Cob}$ of all $2$ -cobordisms. As an application, we show that the local monoids of $2\mathfrak{Cob}$ do not have finitely axiomatizable equational theories. As yet another application, we construct a von-Neumann-regular extension of this category. Similar results are provided for the topological annular category and various quotients of the latter, like the affine Temperley--Lieb category.

Keywords

2-cobordism combinatorial skeleton annular category equational logic local monoid von neumann regular extension

Cite

@article{arxiv.2002.01016,
  title  = {Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic},
  author = {Karl Auinger and Mikhail Volkov},
  journal= {arXiv preprint arXiv:2002.01016},
  year   = {2026}
}

Comments

Version 2 is radically reworked and substantially extended and should therefore be considered essentially a new paper. 95 pages, 13 numbered figures and many unnumbered illustrations, 1 table

Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic

Abstract

Keywords

Cite

Comments

Related papers