Some very low-dimensional algebraic topology
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929603724967936 |
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| author | Morava, J |
| author_facet | Morava, J |
| contents | 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 $X \to ΩS^2$ were proposed in \cite{14} as useful in these contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15885 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some very low-dimensional algebraic topology Morava, J Algebraic Topology 57R56, 11M32 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 $X \to ΩS^2$ were proposed in \cite{14} as useful in these contexts. |
| title | Some very low-dimensional algebraic topology |
| topic | Algebraic Topology 57R56, 11M32 |
| url | https://arxiv.org/abs/2411.15885 |