Manning–Wang dimension conjecture for Bowditch boundaries

Let (G,P)(G,\mathcal{P}) be a type FF relatively hyperbolic group pair, with Bowditch boundary (G,P)\partial(G,\mathcal{P}), and let cd(G,P)\operatorname{cd}(G,\mathcal{P}) denote the cohomological dimension of the pair. Manning–Wang dimension conjecture.

dim(G,P)=cd(G,P)1.\dim\partial(G,\mathcal{P})=\operatorname{cd}(G,\mathcal{P})-1.

This conjecture relates the topological dimension of the Bowditch boundary to the cohomological dimension of the relatively hyperbolic group pair. The source attributes it to Manning and Wang; its resolution is not established by the supplied text.

Sources & referencesView supporting material

Primary source

Oliver H. Wang, “A spectral sequence for Dehn fillings”, arXiv:1806.09470 (2020).

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