Related papers: Examples of disk algebras

We uncover a somewhat surprising connection between spaces of multiplicative maps between $A_\infty$-ring spectra and topological Hochschild cohomology. As a consequence we show that such spaces become infinite loop spaces after looping…

We compute topological Hochschild homology of sufficiently structured forms of truncated Brown--Peterson spectra with coefficients. In particular, we compute $\mathrm{THH}_*(B\langle n\rangle ;H\mathbb{Z}_{(p)})$ for all $n$ and…

We equip $\mathrm{BP} \langle n \rangle$ with an $\mathbb{E}_3$-$\mathrm{BP}$-algebra structure, for each prime $p$ and height $n$. The algebraic $K$-theory of this ring is of chromatic height exactly $n+1$, and the map…

We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the…

We characterize ring spectra morphisms from the algebraic cobordism spectrum $\QTR{Bbb}{MGL}$ (\QCITE{cite}{}{Vo1}) to an oriented spectrum $\QTR{Bbb}{E}$ (in the sense of Morel \QCITE{cite}{}{Mo}) via formal group laws on the…

We note that our stable homotopy refinements of Khovanov's arc algebras and tangle invariants induce refinements of Chen-Khovanov and Stroppel's platform algebras and tangle invariants, and discuss the topological Hochschild homology of…

Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit…

We compute topological Hochschild homology of $\mathbb{E}_3$-MU-algebra forms of the second truncated Brown-Peterson spectrum with Adams summand coefficients at $p=2$ and conditionally at arbitrary primes. We also provide a new…

We prove that algebraic K-theory, topological Hochschild homology and topological cyclic homology satisfy cubical and cosimplicial descent at connective structured ring spectra along 1-connected maps of such ring spectra.

Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule…

We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place entirely in the category of equivariant…

We show that Ravenel's spectrum $X(2)$ is the versal $E_1$-$S$-algebra of characteristic $\eta$. This implies that every $E_1$-$S$-algebra $R$ of characteristic $\eta$ admits an $E_1$-ring map $X(2)\to R$, i.e. an $\mathbb{A}_\infty$…

We consider the change-of-rings spectral sequence as it applies to Hochschild cohomology, obtaining a description of the differentials on the first page which relates it to the multiplicative stucture on cohomology. Using this information,…

In this article, we study the topological Hochschild homology of $\mathbf{E}_3$-forms of truncated Brown-Peterson spectra, taken relative to certain Thom spectra $X(p^n)$ (introduced by Ravenel and used by Devinatz-Hopkins-Smith in the…

Given a function $b$, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges--Rovnyak space $H(b)$. We explore representations of such spaces via descriptions of the…

For every $n\ge 0$, we construct classes in the Brown-Peterson cohomology $BP\langle n \rangle$ of smooth projective complex algebraic varieties which are not in the image of the cycle map from the corresponding motivic Brown-Peterson…

Consider an abstract operator $L$ which acts on monomials $x^n$ according to $L x^n= \lambda_n x^n + \nu_n x^{n-2}$ for $\lambda_n$ and $\nu_n$ some coefficients. Let $P_n(x)$ be eigenpolynomials of degree $n$ of $L$: $L P_n(x) = \lambda_n…

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…

This paper introduces a chain model for the Deligne-Mumford operad formed by homotopically trivializing the circle in a chain model for the framed little disks. We then show that under degeneration of the Hochschild to cyclic cohomology…

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…