Related papers: Eilenberg-MacLane spectra as equivariant Thom spec…

Hopkins and Mahowald gave a simple description of the mod $p$ Eilenberg Mac Lane spectrum $\mathbb{F}_p$ as the free $\mathbb{E}_2$-algebra with an equivalence of $p$ and $0$. We show for each faithful $2$-dimensional representation…

In this short note we study the topological Hoschschild homology of Eilenberg-MacLane spectra for finite cyclic groups. In particular, we show that the Eilenberg-MacLane spectrum H(Z/p^k) is a Thom spectrum for any prime p (except,…

We prove that the $C_2$-equivariant Eilenberg-MacLane spectrum associated to the constant Mackey functor $\underline{\mathbb{F}}_2$ is equivalent to a Thom spectrum over ${\Omega^\rho S^{\rho + 1}}$.

We filter the equivariant Eilenberg Maclane spectrum $H\underline{\mathbb{F}}_p$ using the mod $p$ symmetric powers of the equivariant sphere spectrum, $\mathrm{Sp}_{\mathbb{Z}/p}^{\infty}(\Sigma^{\infty G}S^0)$. When $G$ is a $p$-group, we…

In this paper we compute $RO(G)$-graded homotopy Mackey functors of $H\underline{\mathbb{Z}}$, the Eilenberg-Mac Lane spectrum of the constant Mackey functor of integers for cyclic p-groups and give a complete computation for $G = C_{p^2}$…

A Thom spectrum model for a $C_2$-equivariant analogue of integral Brown--Gitler spectra is established and shown to have a multiplicative property. The $C_2$-equivariant spectra constructed enjoy properties analogous to classical…

Let $G$ be a finite $p$-group. The Eilenberg-Maclane spectrum of the constant Mackey functor $\underline{\mathbb{F}}_p$, denoted $H\underline{\mathbb{F}}_p$, is modeled by the free $\mathbb{F}_p$-module on the $G$-equivariant sphere…

Let $G$ be a finite group. For a based $G$-space $X$ and a Mackey functor $M$, a topological Mackey functor $X\widetilde\otimes M$ is constructed, which will be called the stable equivariant abelianization of $X$ with coefficients in $M$.…

For strongly even $\mathbb{E}_{\infty}^{C_2}$-rings $E$ we show that any homotopy ring map $\mathrm{MU} \to E^e$ lifts to an $\mathbb{E}_{\rho}$-map $\mathrm{MU}_{\mathbb{R}} \to E$. This refines the Hahn-Shi Real orientations of Lubin-Tate…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

We show that a large number of Thom spectra, i.e. colimits of morphisms $BG\to BGL_1(\mathbb{S})$, can be obtained as iterated Thom spectra, i.e. colimits of morphisms $BG\to BGL_1(Mf)$ for some Thom spectrum $Mf$. This leads to a number of…

We investigate implications of an old conjecture in unstable homotopy theory related to the Cohen-Moore-Neisendorfer theorem and a conjecture about the $\mathbf{E}_{2}$-topological Hochschild cohomology of certain Thom spectra (denoted $A$,…

In this paper, we study genuine equivariant factorization homology and its interaction with equivariant Thom spectra, which we construct using the language of parametrized higher category theory. We describe the genuine equivariant…

We discuss the Bousfield localization $L_E X$ for any spectrum $E$ and any $HR$-module $X$, where $R$ is a ring with unit. Due to the splitting property of $HR$-modules, it is enough to study the localization of Eilenberg-Mac Lane spectra.…

We compute the dual Steenrod algebra for Bredon homology with constant coefficients $\underline{\mathbb Z}$ and $\underline{\mathbb Z}/2$ in the category of modules over $MU^{((G))}$, the norm to $G=C_{2^n}$ of $MU_{\mathbb R}$. Using this…

We compute the $RO(G)$-graded equivariant algebraic $K$-groups of a finite field with an action by its Galois group $G$. Specifically, we show these $K$-groups split as the sum of an explicitly computable term and the well-studied…

In this survey paper on commutative ring spectra we present some basic features of commutative ring spectra and discuss model category structures. As a first interesting class of examples of such ring spectra we focus on (commutative)…

We compute the slices and slice spectral sequence of integral suspensions of the equivariant Eilenberg-Mac Lane spectra $H\underline{\mathbb{Z}}$ for the group of equivariance $Q_8$. Along the way, we compute the Mackey functors…

We prove definable versions of the Universal Coefficient Theorems of Eilenberg--Mac Lane expressing the (Steenrod) homology groups of a compact metrizable space in terms of its integral cohomology groups, and the (\v{C}ech) cohomology…

We extend Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation is a computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The result we obtain…