Anick's Sullivan-model conjecture

Let (ΛW,d)(\Lambda W,\operatorname{d}) be a minimal Sullivan algebra with dimW<\dim W<\infty, W1=0W^1=0, and fix nNn\in\mathbb{N}. A relative Sullivan algebra (ΛWΛV,d)(\Lambda W\otimes\Lambda V,\operatorname{d}) is elliptic when its relevant cohomology and generating space are finite dimensional, and it is minimal as a non-relative Sullivan algebra in the stated sense when the relative construction is also minimal after forgetting the base. Anick's Sullivan-model conjecture. There is an elliptic relative Sullivan algebra (ΛWΛV,d)(\Lambda W\otimes\Lambda V,\operatorname{d}) which is even minimal as a non-relative Sullivan algebra and satisfies V=VnV=V^{\geq n}. The source presents this as a Sullivan-algebra reformulation of Anick's conjecture; no resolution is stated in the supplied text.

Sources & referencesView supporting material

Primary source

Manuel Amann, “The Omnibus Conjecture—disproved”, arXiv:2011.01827 (2020).

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