ScalingStacks

0N2T

Theorem 1.2. There is an equivalence between homology theories for topological nn-manifolds valued in 𝒱\mathcal{V} and nn-disk algebras in 𝒱\mathcal{V}

∫:π– π—…π—€π’Ÿβ€‹π—‚π—Œπ—„π—‡β‘(𝒱)\textstyle{\displaystyle\int:\Alg_{\disk_{n}}(\mathcal{V})\ignorespaces\ignorespaces\ignorespaces\ignorespaces}𝐇⁑(ℳ​𝖿𝗅𝖽n,𝒱):𝖾𝗏ℝn.\textstyle{\mathbf{H}(\mfld_{n},\mathcal{V}):{\sf ev}_{\mathbb{R}^{n}}~.\ignorespaces\ignorespaces\ignorespaces\ignorespaces}

This equivalence is implemented by the factorization homology functor ∫\int from the left, and evaluation on ℝn\mathbb{R}^{n} from the right.

Original mathematics by the credited authors. Source collection and HTML conversion remain in progress.

David Ayala, John Francis

Original source: arXiv:1206.5522v6