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Let $G$ be a discrete group. We prove that the category of $G$-posets admits a model structure that is Quillen equivalent to the standard model structure on $G$-spaces. As is already true nonequivariantly, the three classes of maps defining the model structure are not well understood calculationally. To illustrate, we exhibit some examples of cofibrant and fibrant posets and an example of a non-cofibrant finite poset.
We introduce and compare two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category. For the topological model category of spaces, we generalize Piacenzas result that the categories of topological presheaves ind
We define in the setting of homotopy type theory an H-space structure on $mathbb S^3$. Hence we obtain a description of the quaternionic Hopf fibration $mathbb S^3hookrightarrowmathbb S^7twoheadrightarrowmathbb S^4$, using only homotopy invariant tools.
We investigate certain adjunctions in derived categories of equivariant spectra, including a right adjoint to fixed points, a right adjoint to pullback by an isometry of universes, and a chain of two right adjoints to geometric fixed points. This lea
Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some of the mo
We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Diecks splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equiv