In this article, the author places Marxist scholarship in conversation with critical Indigenous theory, outlining Marx's insights and tracing recent development within Marxist-feminist literature before critiquing this scholarship from the perspective of critical Indigenous theory. The author argues that the failure to attend to Indigenous sovereignties is a critical limitation undermining attempts to theorize multiple systems of oppression, demonstrating that critical Indigenous theory, with its more expansive understanding of relationality, not only addresses this limitation but also extends the theorization beyond the logic of capital.
Let $(Z,d,\mu)$ be a compact, connected, Ahlfors $Q$-regular metric space with $Q>1$. Using a hyperbolic filling of $Z$, we define the notions of the $p$-capacity between certain subsets of $Z$ and of the weak covering $p$-capacity of path families $\Gamma$ in $Z$. We show comparability results and quasisymmetric invariance. We reprove a result due to Tyson on the geometric quasiconformality of quasisymmetric maps between compact, connected, Ahlfors $Q$-regular metric spaces. Under certain conditions, we identify the Ahlfors regular conformal dimension of $Z$ with critical exponents arising from weak capacity. Following an approach by Mario Bonk and Bruce Kleiner, we prove a necessary and sufficient condition involving weak capacity for an Ahlfors regular metric space that is topologically $\mathbb{S}^2$ to be quasisymmetrically equivalent to $\mathbb{S}^2$.
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