Algebraic presentation of the bordism category of 2-dimensional CW-complexes

Ivelina Bobtcheva

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arXiv · 2309.04830

Algebraic presentation of the bordism category of 2-dimensional CW-complexes

Ivelina Bobtcheva

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Abstract

We prove that $S^1$ carries the structure of a unimodular cocommutative Hopf algebra in the bordism category 2CW of 2-equivalence classes of 2-dimensional CW-complexes and that 2CW is actually equivalent to the symmetric monoidal category freely generated by such a Hopf algebra. The proof proceeds by constructing an equivalence between 2CW and a category of finite relative group presentations. Finally, we show that the algebraic structure of the category 4HB of 2-equivalence classes of orientable 4-dimensional 2-handlebodies refines that of 2CW.

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BibTeX RIS

Ivelina Bobtcheva. 2026-09-11. Algebraic presentation of the bordism category of 2-dimensional CW-complexes. https://arxiv.org/abs/2309.04830

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