Cone decomposition conjecture with Euclidean factors

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Let ZZ be the conical manifold and let \targetcat\targetcat be the target category appearing in the cone decomposition theorem. For each integer d≥0d\geq 0, consider the restriction functors between categories of constructible factorization algebras associated to the cone \topconeZ\topcone{Z}, its open part Z×(0,∞)Z\times(0,\infty), the half-line [0,∞)[0,\infty), and (0,∞)(0,\infty), after taking products with Rd\reals^d. The rightmost vertical functor sends an object \Aa\Aa to its factorization-algebra integral ∫Z\Aa\int_Z\Aa. Cone decomposition conjecture with Euclidean factors. In the setting of the cone decomposition theorem, the square

\begin{tikzcd} \FactCstr[\targetcat]{\topcone{Z}\times\reals^d} \arrow{d}{\pf{p}} \arrow{r} \isCartesian & \FactCstr[\targetcat]{Z\times(0,\infty)\times\reals^d} \arrow{d}{\pf{p}} & \Aa \ar[d,\mapsto] \\ \FactCstr[\targetcat]{[0,\infty)\times\reals^d} \arrow{r} & \FactCstr[\targetcat]{(0,\infty)\times\reals^d} & \int_Z\Aa \end{tikzcd}

is a pullback square for each d≥0d\geq 0. This globalization conjecture would assemble constructible factorization algebras on smooth conical manifolds from algebras and modules on their smooth strata; it follows from the cone decomposition theorem once additivity for products with Rd\reals^d is established, and the paper does not prove it.

References

Primary source

Eilind Karlsson, Claudia I. Scheimbauer and Tashi Walde, “Assembly of Constructible Factorization Algebras”, arXiv:2403.19472 (2025).

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