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Related papers: Cyclic homology for bornological coarse spaces

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We study a naturally occurring $E_{\infty}$-subalgebra of the full $E_2$-Hochschild cochain complex arising from coherent cochains. For group rings and certain category algebras, these cochains detect $H^*(B {\cal{C}})$, the simplicial…

Algebraic Topology · Mathematics 2018-02-12 Jerry Lodder

In the present paper the cyclic homology functor from the category of $A_\infty$-algebras over any commutative unital ring $K$ to the category of graded $K$-modules is constructed. Further, it is showed that this functor sends homotopy…

Algebraic Topology · Mathematics 2019-05-28 S. V. Lapin

We introduce the notion of an E_k-ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories.…

Algebraic Topology · Mathematics 2025-06-11 John Rognes , Steffen Sagave , Christian Schlichtkrull

Let k be a commutative algebra with the field of the rational numbers included in k and let (E,p,i) be a cleft extension of A. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of E…

K-Theory and Homology · Mathematics 2015-07-08 Jorge A. Guccione , Juan J. Guccione , Christian Valqui

We define the appropriate homological setting to study deformation theory of complete locally convex (curved) dg-algebras based on Positselski's contraderived categories. We define the corresponding Hochschild complex controlling…

Quantum Algebra · Mathematics 2025-12-25 Patrick Antweiler

We generalize the notion of a bornology by omitting the condition that a one-point-subset is bounded and obtain a complete and co-complete generalization of the category of bornological coarse spaces. Then we imitate the construction of…

Algebraic Topology · Mathematics 2019-07-10 Daniel Heiss

A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…

funct-an · Mathematics 2008-02-03 S. C. Power

$HC_*(A \rtimes G)$ is the cyclic homology of the crossed product algebra $A \rtimes G.$ For any $g \epsilon G$ we will define a homomorphism from $HC_*^g(A),$ the twisted cylic homology of $A$ with respect to $g,$ to $HC_*(A \rtimes G).$…

K-Theory and Homology · Mathematics 2014-03-31 Jack M. Shapiro

A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…

Algebraic Geometry · Mathematics 2015-11-20 Leovigildo Alonso Tarrío , Ana Jeremías López , Joseph Lipman

We study the quotient space obtained by the flip action on the quantum n-tori. The Hochschild, cyclic and periodic cyclic homology are calculated.

K-Theory and Homology · Mathematics 2020-07-09 Safdar Quddus

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of…

Algebraic Topology · Mathematics 2014-11-11 A. J. Blumberg , R. L. Cohen , C. Schlichtkrull

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

K-Theory and Homology · Mathematics 2007-05-23 Wolfgang Lueck , Holger Reich

We identify the periodic cyclic homology of the algebra of complete symbols on a differential groupoid $\GR$ in terms of the cohomology of $S^*(\GR)$, the cosphere bundle of $A(\GR)$, where $A(\GR)$ is the Lie algebroid of $\GR$. We also…

Operator Algebras · Mathematics 2007-05-23 Moulay-Tahar Benameur , Victor Nistor

We view the space of cotraces in the structural coalgebra of a principal coaction as a noncommutative counterpart of the classical Cartan model. Then we define the cyclic-homology Chern-Weil homomorphism by extending the Chern-Galois…

K-Theory and Homology · Mathematics 2017-12-29 Piotr M. Hajac , Tomasz Maszczyk

We propose a category which can serve as the category of coefficients for the cyclic homology HC_*(A) of an associative algebra A over a field k. The construction is categorical in nature, and essentially uses only the tensor category…

K-Theory and Homology · Mathematics 2011-11-09 D. Kaledin

We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic $K$-homology and equivariant…

K-Theory and Homology · Mathematics 2021-05-28 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

We prove an equivariant localization theorem over an algebraically closed field of characteristic zero for smooth quotient stacks by reductive groups $X/G$ in the setting of derived loop spaces as well as Hochschild homology and its cyclic…

Algebraic Geometry · Mathematics 2023-01-12 Harrison Chen

We prove the additive version of the conjecture proposed by Ginzburg and Kaledin. This conjecture states that if X/G is an orbifold modeled on a quotient of a smooth affine symplectic variety X (over C) by a finite group G\subset Aut(X) and…

Quantum Algebra · Mathematics 2007-05-23 Vasiliy Dolgushev , Pavel Etingof

Global intersection theories for smooth algebraic varieties via products in {\it appropriate}\, Poincar\'e duality theories are obtained. We assume given a (twisted) cohomology theory $H^*$ having a cup product structure and we let consider…

alg-geom · Mathematics 2008-02-03 Luca Barbieri-Viale

We quiver-interpret the classical simplicial theory - including the cosimplex category $\Delta$, Dold-Kan correspondence, and Hochschild homology - as a certain Q-homotopy theory of type $A$. For the cyclic and cubical theories, we proceed…

Algebraic Topology · Mathematics 2012-11-28 Jiarui Fei