Algebraic characterisation of the category of cobordisms of 2-dimensional CW-complexes and the Andrews-Curtis conjecture

2023/09/09 by Ivelina Bobtcheva, Bobtcheva, Ivelina
Mathematics · #16T05 #20F05 #57M20 #57Q10 #57R56 #57T05 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2309.04830

openalex publication_date 2023/09/09 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28

Abstract

We prove that S¹ is a unimodular, cocommutative Hopf algebra in the category CW¹⁺¹ of 2-equivalence classes of cobordisms of 2-dimensional CW-complexes and that CW¹⁺¹ is actually equivalent to the symmetric monoidal category freely generated by such Hopf algebra. Moreover, we show that the algebraic structure the category \cal Chb³⁺¹ of cobordisms of orientable relative 4-dimensional 2-handlebody cobordisms up to 2-deformations described in \citeBP12, is a refinement of the algebraic structure of their spines.

Related

• On the algebraic characterization of the category of 3-dimensional cobordisms
• Algebraic Presentation of 4-Dimensional 2-Handlebodies and 3-Dimensional Cobordisms
• Nested cobordisms, Cyl-objects and Temperley-Lieb algebras
• Algebraic cobordism
• Cosovereign Hopf algebras