English
Related papers

Related papers: The algebraic structure of twisted topological Hoc…

200 papers

Twisted topological Hochschild homology of $C_n$-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In…

Algebraic Topology · Mathematics 2021-11-22 Katharine Adamyk , Teena Gerhardt , Kathryn Hess , Inbar Klang , Hana Jia Kong

In this paper, we construct a Real equivariant version of the B\"okstedt spectral sequence which takes inputs in the theory of Real Hochschild homology developed by Angelini-Knoll, Gerhardt, and Hill and converges to the equivariant…

Algebraic Topology · Mathematics 2024-08-15 Chloe Lewis

We show the topological Hochschild homology spectrum of a twisted group algebra $\THH(A^{\tau}[G])$ is the Thom spectrum associated to a parametrized orthogonal spectrum $E(A,G)$. We then analyze the structure of the parametrized orthogonal…

Algebraic Topology · Mathematics 2007-05-23 Daniel J. Vera

The topological Hochschild homology of a ring (or ring spectrum) $R$ is an $S^1$-spectrum, and the fixed points of THH($R$) for subgroups $C_n\subset S^1$ have been widely studied due to their use in algebraic K-theory computations.…

Algebraic Topology · Mathematics 2025-04-17 Anna Marie Bohmann , Teena Gerhardt , Cameron Krulewski , Sarah Petersen , Lucy Yang

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,…

Algebraic Topology · Mathematics 2014-10-01 Vigleik Angeltveit , John Rognes

The topological Hochschild homology $THH(A)$ of an orthogonal ring spectrum $A$ can be defined by evaluating the cyclic bar construction on $A$ or by applying B\"okstedt's original definition of $THH$ to $A$. In this paper, we construct a…

Algebraic Topology · Mathematics 2019-06-20 Emanuele Dotto , Cary Malkiewich , Irakli Patchkoria , Steffen Sagave , Calvin Woo

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…

Algebraic Topology · Mathematics 2024-08-28 Gabriel Angelini-Knoll , Dominic Leon Culver , Eva Höning

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…

K-Theory and Homology · Mathematics 2016-10-04 V. Angeltveit , A. Blumberg , T. Gerhardt , M. Hill , T. Lawson , M. Mandell

Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, and Bohmann-Gerhardt-H{\o}genhaven-Shipley-Ziegenhagen developed a coB\"okstedt spectral sequence to compute the homology of coTHH for…

Algebraic Topology · Mathematics 2021-08-19 Sarah Klanderman

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…

Algebraic Topology · Mathematics 2020-04-29 Eva Höning

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…

Algebraic Topology · Mathematics 2024-12-24 Andrew J. Blumberg , Michael A. Mandell , Allen Yuan

The cyclic bar construction in symmetric spectra and B\"okstedt's original construction are two possible ways to define the topological Hochschild homology of a symmetric ring spectrum. In this short note we explain how to correct an error…

Algebraic Topology · Mathematics 2016-07-06 Irakli Patchkoria , Steffen Sagave

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,…

Algebraic Topology · Mathematics 2008-11-06 Andrew J. Blumberg

We study the C_p-equivariant Tate construction on the topological Hochschild homology THH(B) of a symmetric ring spectrum B by relating it to a topological version R_+(B) of the Singer construction, extended by a natural circle action. This…

Algebraic Topology · Mathematics 2022-06-22 Sverre Lunøe--Nielsen , John Rognes

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…

Algebraic Topology · Mathematics 2014-10-01 M. Brun , Z. Fiedorowicz , R. M. Vogt

We propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the $p$-local integers. For the tamely ramified extension of…

Algebraic Topology · Mathematics 2020-08-12 Bjørn Ian Dundas , Ayelet Lindenstrauss , Birgit Richter

We discuss spectral sequences coming from Whitehead filtrations in the computation of topological Hochschild homology of ring spectra. Using cyclic invariance, this makes for simple computations of $THH$ of connective rings $R$ with…

Algebraic Topology · Mathematics 2025-07-23 Logan Hyslop

Let A be an A_\infty ring spectrum. We use the description from [2] of the cyclic bar and cobar construction to give a direct definition of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another…

Algebraic Topology · Mathematics 2014-11-11 Vigleik Angeltveit

We study the homology of free loop spaces via techniques arising from the theory of topological coHochschild homology (coTHH). Topological coHochschild homology is a topological analogue of the classical theory of coHochschild homology for…

Algebraic Topology · Mathematics 2021-12-15 Anna Marie Bohmann , Teena Gerhardt , Brooke Shipley

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…

Algebraic Topology · Mathematics 2021-07-14 Eva Höning
‹ Prev 1 2 3 10 Next ›