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Related papers: Total power operations in spectral sequences

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Power operations in the homology of infinite loop spaces, and $H_\infty$ or $E_\infty$ ring spectra have a long history in Algebraic Topology. In the case of ordinary mod p homology for a prime p, the power operations of Kudo, Araki, Dyer…

Algebraic Topology · Mathematics 2014-12-19 Andrew Baker

We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The definition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soule, by…

K-Theory and Homology · Mathematics 2009-06-09 Elisenda Feliu

In this survey paper, we will collate various different ideas and thoughts regarding equivariant operations on quantum cohomology (and some in more general Floer theory) for a symplectic manifold. We will discuss a general notion of…

Symplectic Geometry · Mathematics 2024-09-30 Nicholas Wilkins

We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of…

Algebraic Topology · Mathematics 2023-02-09 Fernando Muro

We use the Adams spectral sequence to compute the KO-theory of all toric manifolds and certain singular toric varieties.

Algebraic Topology · Mathematics 2007-05-23 Anthony Bahri , Martin Bendersky

We study the stability of quasinormal modes (QNMs) in electrically charged black brane spacetimes that asymptote to AdS by means of the pseudospectrum. Methodologically, we adopt ingoing Eddington-Finkelstein coordinates to cast QNMs in…

General Relativity and Quantum Cosmology · Physics 2024-11-07 Brad Cownden , Christiana Pantelidou , Miguel Zilhão

We propose a method for calculating cohomology operations for finite simplicial complexes. Of course, there exist well--known methods for computing (co)homology groups, for example, the reduction algorithm consisting in reducing the…

Algebraic Topology · Mathematics 2011-05-19 Rocio Gonzalez-Diaz , Pedro Real

Let $p$ be a prime, let $KU_p$ be $p$-complete complex $K$-theory, and let $\mathbb{Z}_p^\times$ denote the group of units in the $p$-adic integers. The $p$-adic Adams operations induce an action of the profinite group $\mathbb{Z}_p^\times$…

Algebraic Topology · Mathematics 2023-08-07 Daniel G. Davis

Let V(0) be the mod 2 Moore spectrum and let C be the supersingular elliptic curve over F_4 defined by the Weierstrass equation y^2+y=x^3. Let F_C be its formal group law and E_C be the spectrum classifying the deformations of F_C. The…

Algebraic Topology · Mathematics 2017-02-03 Agnes Beaudry

We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…

Algebraic Topology · Mathematics 2010-02-12 Daniel C. Isaksen , Armira Shkembi

We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of…

Strongly Correlated Electrons · Physics 2007-05-23 J. M. P. Carmelo , K. Penc

We demonstrate that an equidistant area spectrum for the link variables in loop quantum gravity can reproduce both the thermodynamics and the quasinormal mode properties of black holes.

High Energy Physics - Theory · Physics 2009-11-10 Alexios P. Polychronakos

We extend the Cisinski-Moerdijk-Weiss theory of $\infty$-operads to the equivariant setting to obtain a notion of $G$-$\infty$-operads that encode "equivariant operads with norm maps" up to homotopy. At the root of this work is the…

Algebraic Topology · Mathematics 2018-05-02 Luis Alexandre Pereira

A co-operational bivariant theory is a ``dual" version of Fulton--MacPherson's operational bivaiant theory. For a given contravariant functor we define a generalized cohomology operation for continuous maps having sections, using cohomology…

Algebraic Topology · Mathematics 2025-07-11 Shoji Yokura

We describe a variant construction of the unstable Adams spectral the sequence for a space $Y$, associated to any free simplicial resolution of $H^*(Y;R)$ for $R=\mathbb{F}_p$ or $\mathbb{Q}$. We use this construction to describe the…

Algebraic Topology · Mathematics 2017-09-05 Samik Basu , David Blanc , Debasis Sen

We determine all natural operations and their relations on the homotopy groups of spectral partition Lie algebras, which coincide with $\mathbb{F}_p$-linear topological Andr\'{e}-Quillen cohomology operations at any prime. We construct…

Algebraic Topology · Mathematics 2025-05-06 Adela YiYu Zhang

We show that the family of Podles' spheres is complete under equivariant Morita equivalence (with respect to the action of quantum SU(2)), and determine the associated orbits. We also give explicit formulas for the actions which are…

Quantum Algebra · Mathematics 2013-08-13 K. De Commer

Given a finite abelian group $G$ and a Sylow $p$-subgroup $N_p$, we prove that the $KU_G/p$-local sphere spectrum is equivalent to the homotopy fixed points of a $p$-complete $KO_{N_p}$-module spectrum. Then we compute the…

Algebraic Topology · Mathematics 2026-05-29 Yingxin Li

Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…

Category Theory · Mathematics 2026-01-27 Shih-Yu Chang

Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…

High Energy Physics - Theory · Physics 2009-10-31 M. Bojowald , H. A. Kastrup