Related papers: The spectrum for commutative complex $K$-theory

In this article we describe the $G_{comp}\times G_{comp}$-equivariant topological $K$-ring of a {\em cellular} toroidal embedding $\mathbb{X}$ of a complex connected reductive algebraic group $G$. In particular, our results extend the…

Cohomological and K-theoretic stable bases originated from the study of quantum cohomology and quantum K-theory. Restriction formula for cohomological stable bases played an important role in computing the quantum connection of cotangent…

We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence…

We show that the category of rational G-spectra for a torus G is Quillen equivalent to an explicit small and practical algebraic model, thereby providing a universal de Rham model for rational G-equivariant cohomology theories. The result…

With $G = \mathbb{Z}/p$, $p$ prime, we calculate the ordinary $G$-cohomology (with Burnside ring coefficients) of $\mathbb{C}P_G^\infty = B_G U(1)$, the complex projective space, a model for the classifying space for $G$-equivariant complex…

Billey and Braden defined a geometric pattern map on flag manifolds which extends the generalized pattern map of Billey and Postnikov on Weyl groups. The interaction of this torus equivariant map with the Bruhat order and its action on line…

In this paper we develop methods for classifying Baker-Richter-Szymik's Azumaya algebras over a commutative ring spectrum, especially in the largely inaccessible case where the ring is nonconnective. We give obstruction-theoretic tools,…

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside…

In this paper we study the "holomorphic K-theory" of a projective variety, which is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory was introduced by Lawson,…

In this note, we show that the algebraic K-theory of generalized archimedean valuation rings occurring in Durov's compactification of the spectrum of a number ring is given by stable homotopy groups of certain classifying spaces. We also…

We compute the homotopy groups of $\mathrm{THH}(\mathrm{ku})$ as a $\mathrm{ku}_\ast$-module using the descent spectral sequence for the map $\mathrm{THH}(\mathrm{ku})\to\mathrm{THH}(\mathrm{ku}/\mathrm{MU})$, which is the motivic spectral…

Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These…

We consider infinite tensor product actions of $G = \mathbb{Z}/p\mathbb{Z}$ on the UHF-algebra $D = \text{End}(V)^{\otimes \infty}$ for a finite-dimensional unitary $G$-representation $V$ and determine the equivariant homotopy type of the…

We prove that the equivariant big quantum cohomology QH^*_T(E) of the total space of a toric bundle E \to B converges provided that the big quantum cohomology QH^*(B) converges. The proof is based on Brown's mirror theorem for toric…

We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…

Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real K-theory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for…

Let $X$ be a torus manifold with locally standard action of a compact torus $T$ of half the dimension and orbit space a homology polytope. Smooth complete complex toric varieties and quasi-toric manifolds are examples of torus manifolds.…

We define equivariant projective unitary stable bundles as the appropriate twists when defining K-theory as sections of bundles with fibers the space of Fredholm operators over a Hilbert space. We construct universal equivariant projective…

We construct a ``logarithmic'' cohomology operation on Morava E-theory, which is a homomorphism defined on the multiplicative group of invertible elements in the ring E^0(K) of a space K. We obtain a formula for this map in terms of the…

If H is a commutative connected graded Hopf algebra over a commutative ring k, then a certain canonical k-algebra homomorphism H -> H (x) QSym is defined, where QSym denotes the Hopf algebra of quasisymmetric functions over k. This…