Abstract
Bott, Cattaneo and Rossi defined invariants of long knots $\mathbb{R}^{n} \hookrightarrow \mathbb{R}^{n+2}$ as combinations of configuration space integrals for $n$ odd $\geq 3$. Here, we give a more flexible definition of these invariants. Our definition allows us to interpret these invariants as counts of diagrams. It extends to long knots inside more general $(n+2)$-manifolds, called asymptotic homology $\mathbb{R}^{n+2}$, and provides invariants of these knots.
Citation
David LETURCQ. "Generalized Bott–Cattaneo–Rossi invariants of high-dimensional long knots." J. Math. Soc. Japan 73 (3) 815 - 860, July, 2021. https://doi.org/10.2969/jmsj/82908290
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