2020/02/03 by Karl Auinger, Mikhail V. Volkov, Auinger, Karl +1
Mathematics · #20M07 08B05 18B40 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2002.01016
openalex publication_date 2020/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a complete set of combinatorial data that encode the category 2\mathfrakCob of all 2-cobordisms. As an application, we show that the local monoids of 2\mathfrakCob 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.