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

Ivelina Bobtcheva

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arXiv · 2309.04830

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

Ivelina Bobtcheva

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Abstract

We prove that $S^1$ is a unimodular, cocommutative Hopf algebra in the category $CW^{1+1}$ of 2-equivalence classes of cobordisms of 2-dimensional CW-complexes and that $CW^{1+1}$ is actually equivalent to the symmetric monoidal category freely generated by such Hopf algebra. Moreover, we show that the algebraic structure the category ${\cal C}hb^{3+1}$ of cobordisms of orientable relative 4-dimensional 2-handlebody cobordisms up to 2-deformations described in \cite{BP12}, is a refinement of the algebraic structure of their spines.

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BibTeX RIS

Ivelina Bobtcheva. 2023-09-09. Algebraic characterisation of the category of cobordisms of 2-dimensional CW-complexes and the Andrews-Curtis conjecture. https://arxiv.org/abs/2309.04830

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