Related papers: Units of ring spectra and their traces in algebrai…

The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show,…

We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…

We identify the topological Hochschild homology (THH) of the Thom spectrum associated to an E_\infty classifying map X -> BG, for G an appropriate group or monoid (e.g. U, O, and F). We deduce the comparison from the observation of McClure,…

We review and extend the theory of Thom spectra and the associated obstruction theory for orientations. We recall (from May, Quinn, and Ray) that a commutative ring spectrum A has a spectrum of units gl(A). To a map of spectra f: b ->…

We give an operator algebraic model for the first group of the unit spectrum $gl_1(KU)$ of complex topological K-theory, i.e. $[X, BGL_1(KU)]$, by bundles of stabilized infinite Cuntz C*-algebras $O_{\infty} \otimes \K$. We develop similar…

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)…

Let $K(\mathbb{F}_q)$ be the algebraic $K$-theory spectrum of the finite field with $q$ elements and let $p \geq 5$ be a prime number coprime to $q$. In this paper we study the mod $p$ and $v_1$ topological Hochschild homology of…

The $2$-primary Hopf invariant $1$ elements in the stable homotopy groups of spheres form the most accessible family of elements. In this paper we explore some properties of the $\mathcal{E}_\infty$ ring spectra obtained from certain…

We study commutative complex $K$-theory, a generalised cohomology theory built from spaces of ordered commuting tuples in the unitary groups. We show that the spectrum for commutative complex $K$-theory is stably equivalent to the…

For a commutative ring R with many units, we describe the kernel of H_3(inc): H_3(GL_2(R), Z) --> H_3(GL_3(R), Z). Moreover we show that the elements of this kernel are of order at most two. As an application we study the indecomposable…

Using an analogy between the Brauer groups in algebra and the Whitehead groups in topology, we first use methods of algebraic K-theory to give a natural definition of Brauer spectra for commutative rings, such that their homotopy groups are…

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…

In this work we study the $E_{\infty}$-ring $\text{THH}(\mathbb{F}_p)$ as a graded spectrum. Following an identification at the level of $E_2$-algebras with $\mathbb{F}_p[\Omega S^3]$, the group ring of the $E_1$-group $\Omega S^3$ over…

We describe a structure on a commutative ring (pre)cyclotomic spectrum $R$ that gives rise to a (pre)cyclotomic structure on topological Hochschild homology ($THH$) relative to its underlying commutative ring spectrum. This lets us…

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.

The main result of this paper is the computation of TR^n_{\alpha}(F_p;p) for \alpha in R(S^1). These R(S^1)-graded TR-groups are the equivariant homotopy groups naturally associated to the S^1-spectrum THH(F_p), the topological Hochschild…

We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like…

We show that the topological Hochschild homology THH(R of an E_n-ring spectrum R is an E_{n-1}-ring spectrum. The proof is based on the fact that the tensor product of the operad Ass for monoid structures and the the little n-cubes operad…

Topological Hochschild homology (THH) is an invariant of ring spectra developed by B\"okstedt. In recent years many equivariant analogues to THH have emerged. One example is twisted THH which is an invariant of $C_n$-equivariant ring…

We generalize a spectral sequence of Brun for the computation of topological Hochschild homology. The generalized version computes the $E$-homology of $THH(A;B)$, where $E$ is a ring spectrum, $A$ is a commutative $S$-algebra and $B$ is a…