Algebras of the cohomology operations in some cohomology theories

A. Jankowski

Displaying similar documents to “Algebras of the cohomology operations in some cohomology theories”

$L^{2}$ -cohomology

J. Eichhorn (1986)

Banach Center Publications

Similarity:

A review of Lie superalgebra cohomology for pseudoforms

Carlo Alberto Cremonini (2022)

Archivum Mathematicum

Similarity:

This note is based on a short talk presented at the “42nd Winter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational...

Overconvergent de Rham-Witt cohomology

Christopher Davis, Andreas Langer, Thomas Zink (2011)

Annales scientifiques de l'École Normale Supérieure

Similarity:

The goal of this work is to construct, for a smooth variety $X$ over a perfect field k of finite characteristic $p > 0$ , an overconvergent de Rham-Witt complex $W^{†} Ω_{X / k}$ as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in $X$ , is a complex of étale sheaves and a differential graded algebra over the ring $W^{†} (𝒪_{X})$ of overconvergent Witt-vectors. If $X$ is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

Motivic cohomology and unramified cohomology of quadrics

Bruno Kahn, R. Sujatha (2000)

Journal of the European Mathematical Society

Similarity:

This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension $\leq 4$ and $\geq 11$ . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real...

Bounded cohomology of lattices in higher rank Lie groups

Marc Burger, Nicolas Monod (1999)

Journal of the European Mathematical Society

Similarity:

We prove that the natural map $H_{b}^{2} (Γ) \to H^{2} (Γ)$ from bounded to usual cohomology is injective if $Γ$ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for $Γ$ : the stable commutator length vanishes and any $C^{1}$ –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating $H^{*} b (Γ)$ to the continuous bounded cohomology of the...

Local-global principle for annihilation of general local cohomology

J. Asadollahi, K. Khashyarmanesh, Sh. Salarian (2001)

Colloquium Mathematicae

Similarity:

Let A be a Noetherian ring, let M be a finitely generated A-module and let Φ be a system of ideals of A. We prove that, for any ideal in Φ, if, for every prime ideal of A, there exists an integer k(), depending on , such that $^{k ()}$ kills the general local cohomology module $H_{Φ_{}}^{j} (M_{})$ for every integer j less than a fixed integer n, where $Φ_{} : =_{} : \in Φ$ , then there exists an integer k such that $^{k} H_{Φ}^{j} (M) = 0$ for every j < n.

Artinianness of formal local cohomology modules

Shahram Rezaei (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $𝔞$ be an ideal of Noetherian local ring $(R, 𝔪)$ and $M$ a finitely generated $R$ -module of dimension $d$ . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to $𝔪$ . Also we prove that for an arbitrary local ring $(R, 𝔪)$ (not necessarily complete), we have ${Att}_{R} (𝔉_{𝔞}^{d} (M)) = Min V ({Ann}_{R} 𝔉_{𝔞}^{d} (M)) .$

Quantum Cohomology and Crepant Resolutions: A Conjecture

Tom Coates, Yongbin Ruan (2013)

Annales de l’institut Fourier

Similarity:

We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold $𝒳$ to the quantum cohomology of a crepant resolution $Y$ of $𝒳$ . We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines...

Particles in the superworldline and BRST

Eugenia Boffo (2022)

Archivum Mathematicum

Similarity:

In this short note we discuss $N$ -supersymmetric worldlines of relativistic massless particles and review the known result that physical spin- $N / 2$ fields are in the first BRST cohomology group. For $N = 1, 2, 4$ , emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background. ...

Chen–Ruan Cohomology of $ℳ_{1, n}$ and ${\bar{ℳ}}_{1, n}$

Nicola Pagani (2013)

Annales de l’institut Fourier

Similarity:

In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable $n$ -pointed curves of genus $1$ . In the first part of the paper we study and describe stack theoretically the twisted sectors of $ℳ_{1, n}$ and ${\bar{ℳ}}_{1, n}$ . In the second part, we study the orbifold intersection theory of ${\bar{ℳ}}_{1, n}$ . We suggest a definition for an orbifold tautological ring in genus $1$ , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.

Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type $𝐀_{1}$

Bo Hou, Yanhong Guo (2015)

Czechoslovak Mathematical Journal

Similarity:

The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let $Λ_{t}$ be the Yoneda algebra of a reconstruction algebra of type $𝐀_{1}$ over a field $. I n t h i s p a p e r, a m i n i m a l p r o j e c t i v e b i m o d u l e r e s o l u t i o n o f$ t $i s c o n s t r u c t e d, a n d t h e$ -dimensions of all Hochschild homology and cohomology groups of $Λ_{t}$ are calculated explicitly.

Quintasymptotic primes, local cohomology and ideal topologies

A. A. Mehrvarz, R. Naghipour, M. Sedghi (2006)

Colloquium Mathematicae

Similarity:

Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by ${I_{a}}_{I \in Φ}$ and ${S (I_{a})}_{I \in Φ}$ are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then $H_{Φ}^{d} (R)$ , the dth local cohomology module of R with respect to Φ, vanishes if and only if there...

Noetherian loop spaces

Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)

Journal of the European Mathematical Society

Similarity:

The class of loop spaces of which the mod $p$ cohomology is Noetherian is much larger than the class of $p$ -compact groups (for which the mod $p$ cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as $ℂ P^{\infty}$ and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space $B X$ of such an object and prove it is as small as expected, that is, comparable to that of $B ℂ P^{\infty}$ . We also show that $B$ X differs basically from the classifying space of a $p$ -compact...

Fredholm spectrum and growth of cohomology groups

Jörg Eschmeier (2008)

Studia Mathematica

Similarity:

Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let $σ_{F} (T) = σ (T) ∖ σ_{e} (T)$ be the non-essential spectrum of T. We show that, for each connected component M of the manifold $R e g (σ_{F} (T))$ of all smooth points of $σ_{F} (T)$ , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups $H^{p} ({(z - T)}^{k}, E)$ grow at least like the sequence ${(k^{d})}_{k \geq 1}$ with d = dim M.

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Luc Menichi (2009)

Bulletin de la Société Mathématique de France

Similarity:

Let $M$ be any compact simply-connected oriented $d$ -dimensional smooth manifold and let $𝔽$ be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of $M$ , $H H^{*} (S^{*} (M), S^{*} (M))$ , extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjectured to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on $M$ , $H_{* + d} (L M)$ introduced by Chas and Sullivan. We also show that the negative cyclic...

Bounded cohomology and isometry groups of hyperbolic spaces

Ursula Hamenstädt (2008)

Journal of the European Mathematical Society

Similarity:

Let $X$ be an arbitrary hyperbolic geodesic metric space and let $Γ$ be a countable subgroup of the isometry group $Iso (X)$ of $X$ . We show that if $Γ$ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups $H_{b}^{2} (Γ, ℝ)$ , $H_{b}^{2} (Γ, ℓ^{p} (Γ))$ $(1 < p < \infty)$ are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct...

Редуцированные $L_{p}$ -когомологии искривленных цилиндров.

В.М. Гольдштейн, В.И. Кузьминов, И.А. Шведов (1990)

Sibirskij matematiceskij zurnal

Similarity:

Cohomological dimension filtration and annihilators of top local cohomology modules

Ali Atazadeh, Monireh Sedghi, Reza Naghipour (2015)

Colloquium Mathematicae

Similarity:

Let denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration $= {M_{i}}_{i = 0}^{c}$ , where c = cd(,M) and $M_{i}$ denotes the largest submodule of M such that $c d (, M_{i}) \leq i$ . Some properties of this filtration are investigated. In particular, if (R,) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module $H_{}^{c} (M)$ , namely $A n n_{R} (H_{}^{c} (M)) = A n n_{R} (M / M_{c - 1})$ . As a consequence, there exists an ideal of R such that $A n n_{R} (H_{}^{c} (M)) = A n n_{R} (M / H ⁰_{} (M))$ . This generalizes the...

A note on the cohomology ring of the oriented Grassmann manifolds ${\tilde{G}}_{n, 4}$

Tomáš Rusin (2019)

Archivum Mathematicum

Similarity:

We use known results on the characteristic rank of the canonical $4$ –plane bundle over the oriented Grassmann manifold ${\tilde{G}}_{n, 4}$ to compute the generators of the $ℤ_{2}$ –cohomology groups $H^{j} ({\tilde{G}}_{n, 4})$ for $n = 8, 9, 10, 11$ . Drawing from the similarities of these examples with the general description of the cohomology rings of ${\tilde{G}}_{n, 3}$ we conjecture some predictions.