Some very low-dimensional algebraic topology

J Morava

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arXiv · 2411.15885

Some very low-dimensional algebraic topology

J Morava

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Abstract

The Euclidean renormalization bundle considered in QFT by Connes, Kreimer, and Marcolli has been extended, in a remarkable series of papers by S Agarwala, to Riemannian manifolds $(X,g)$: in particular by the construction of a flat connection on that bundle, regarded as defined over a thickening of $X$ by an infinitesimal disk. The theory of Fourier integral operators on manifolds reconciles dimensional and zeta-function regularization by interpreting this disk as the germ of a neighborhood of a Jordan curve around $\infty$ on the Riemann sphere. Such fields $X \to \Omega S^2$ were proposed in \cite{14} as useful in these contexts.

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J Morava. 2024-11-24. Some very low-dimensional algebraic topology. https://arxiv.org/abs/2411.15885

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