Related papers: The Omega spectrum for mod 2 KO-theory

Let $p$ be an odd prime and let $\mathit{EO} = E_{p-1}^{hC_p}$ be the $C_p$ fixed points of height $p-1$ Morava $E$ theory. We say that a spectrum $X$ has algebraic $\mathit{EO}$ theory if the splitting of $K_*(X)$ as an $K_*[C_p]$-module…

We consider $G=Q_8,SD_{16},G_{24},$ and $G_{48}$ as finite subgroups of the Morava stabilizer group which acts on the height $2$ Morava $E$-theory $\mathbf{E}_2$ at the prime $2$. We completely compute the $G$-homotopy fixed point spectral…

Let n \geq 1 and let p be any prime. Also, let E_n be the Lubin-Tate spectrum, G_n the extended Morava stabilizer group, and K(n) the nth Morava K-theory spectrum. Then work of Devinatz and Hopkins and some results due to Behrens and the…

Let $n \geq 1$, $p$ a prime, and $T(n)$ any representative of the Bousfield class of the telescope $v_n^{-1}F(n)$ of a finite type $n$ complex. Also, let $E_n$ be the Lubin-Tate spectrum, $K(E_n)$ its algebraic $K$-theory spectrum, and…

We introduce the Morava-isotropic stable homotopy category and, more generally, the stable homotopy category of an extension $E/k$. These "local" versions of the Morel-Voevodsky stable ${\Bbb{A}}^1$-homotopy category $SH(k)$ are analogues…

We determine the image of the 2-primary tmf-Hurewicz homomorphism, where tmf is the spectrum of topological modular forms. We do this by lifting elements of tmf_* to the homotopy groups of the generalized Moore spectrum M(8,v_1^8) using a…

For an integral cohomology class H of degree n+2 on a space X, we define twisted Morava K-theory K(n)(X; H) at the prime 2, as well as an integral analogue. We explore properties of this twisted cohomology theory, study a twisted…

We compute the $E_2$ page of the Adams spectral sequence converging to the connective KO-theory of the second mod 2 Eilenberg-MacLane space, $ko_*(K(Z/2,2))$. This required a careful analysis of the structure of $H^*(K(Z/2,2);Z_2)$ as a…

Let $A_1$ be any spectrum in a class of finite spectra whose mod $2$ cohomology is isomorphic to a free module of rank one over the subalgebra $\mathcal{A}(1)$ of the Steenrod algebra. Let $E_{C}$ be the second Morava-$E$ theory associated…

We determine the Gross-Hopkins duals of certain higher real $K$-theory spectra. More specifically, let $p$ be an odd prime, and consider the Morava $E$-theory spectrum of height $n=p-1$. It is known, in the expert circles, that for certain…

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show…

We give explicit calculations of the algebraic theory of power operations for a specific Morava E-theory spectrum and its K(1)-localization. These power operations arise from the universal degree-3 isogeny of elliptic curves associated to…

This paper provides conditions for Morava $K$-theory to commute with certain homotopy limits. These conditions extend previous work on this question by allowing for homotopy limits of sequences of spectra that are not uniformly bounded…

The Bousfield-Kan (or unstable Adams) spectral sequence can be constructed for various homology theories such as Brown-Peterson homology theory BP, Johnson-Wilson theory $E(n)$, or Morava $E$-theory $E_n$. For nice spaces the $E_2$-term is…

We compute ko_*(K(Z/2,2)) and ko^*(K(Z/2,2)), the connective KO-homology and -cohomology of the mod 2 Eilenberg-MacLane space K(Z/2,2), using the Adams spectral sequence. The work relies heavily on work done several years earlier for the…

This paper is to construct unstable, Morita stable and stable bivariant algebraic Kasparov $K$-theory spectra of $k$-algebras. These are shown to be homotopy invariant, excisive in each variable $K$-theories. We prove that the spectra…

We define homological dimensions for S-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is…

We calculate the mod (p, v_1, v_2) homotopy V(2)_* TC(BP<2>) of the topological cyclic homology of the truncated Brown--Peterson spectrum BP<2>, at all primes p\ge7, and show that it is a finitely generated and free F_p[v_3]-module on 12p+4…

We use the Adams spectral sequence to compute the KO-theory of all toric manifolds and certain singular toric varieties.

We calculate the integral homotopy groups of THH(l) at any prime and of THH(ko) at p=2, where l is the Adams summand of the connective complex p-local K-theory spectrum and ko is the connective real K-theory spectrum.