Year: 2025
Type: preprint
Abstract: We study the Gelfand-Fuks cohomology of smooth vector fields on $S^d$ relative to $\mathrm{SO}(d+1)$ following a method by Haefliger that uses tools from rational homotopy theory. In particular, we show that $H^*(\mathrm{BSO}(4);\mathbb{R})$ injects into the relative Gelfand-Fuks cohomology which corrects a claim by Haefliger. Moreover, for $S^3$ the relative Gelfand-Fuks cohomology agrees with the smooth cohomology of $\text{Diff}^+(S^3)$ and we provide a computation in low degrees.
Source: arXiv (Cornell University)
Author: Prigge, Nils
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979257803
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