Related papers: On the lambda algebra and Singer's cohomological t…

The rational cohomology of the moduli space of rank two, odd degree stable bundles over a curve (of genus g > 1) has been studied intensely in recent years and in particular the invariant subring generated by Newstead's generators alpha,…

On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e. sections of End(TM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra, A…

Let $X$ be a complex smooth projective variety, and $\mathcal{G}$ a locally free sheaf on $X$. We show that there is a 1-to-1 correspondence between pairs $(\Lambda,\Xi)$, where $\Lambda$ is a sheaf of almost polynomial filtered algebras…

Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point…

The Steenrod squares are cohomology operations with important applications in algebraic topology. While these operations are well-understood classically, little is known about them in the setting of homotopy type theory. Although a…

Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum…

A subalgebra $A$ of the algebra $B(\mathcal{H})$ of bounded linear operators on a separable Hilbert space $\mathcal{H}$ is said to be catalytic if every transitive subalgebra $\mathcal{T}\subset B(\mathcal{H})$ containing it is strongly…

For a transitive Lie algebroid A on a connected manifold M and its a representation on a vector bundle F, we study the localization map Y^1: H^1(A,F)-> H^1(L_x,F_x), where L_x is the adjoint algebra at x in M. The main result in this paper…

Let $\A$ be an arrangement of affine lines in $\C^2,$ with complement $\M(\A).$ The (co)homo-logy of $\M(\A)$ with twisted coefficients is strictly related to the cohomology of the Milnor fibre associated to the conified arrangement,…

When $p$ is an odd prime, we prove that the $\mathbb F_p$-cohomology of $\mathrm{BP}\langle n\rangle$ as a module over the Steenrod algebra determines the $p$-local spectrum $\mathrm{BP}\langle n\rangle$. In particular, we prove that the…

Attributed to J F Adams is the conjecture that, at odd primes, the mod-p cohomology ring of the classifying space of a connected compact Lie group is detected by its elementary abelian p-subgroups. In this note we rely on Toda's calculation…

The purpose of this paper is to investigate an algebraic version of the double complex transfer, in particular the classes in the two-line of the Adams-Novikov spectral sequence which are the image of comodule primitives of the MU-homology…

This paper focuses on the cohomology of operator algebras associated with the free semigroup generated by the set $\{z_{\alpha}\}_{\alpha\in\Lambda}$, with the left regular free semigroup algebra $\mathfrak{L}_{\Lambda}$ and the…

For any $E_\infty$ ring spectrum $E$, we show that there is an algebra $\mathrm{Pow}(E)$ of stable power operations that acts naturally on the underlying spectrum of any $E$-algebra. Further, we show that there are maps of rings $E \to…

We construct and analyze the "syntomic Steenrod algebra", which acts on the mod $p$ syntomic cohomology (also known as etale-motivic cohomology) of algebraic varieties in characteristic $p$. We then apply the resulting theory to resolve the…

Let A be a cosemisimple Hopf *-algebra with antipode S and let $\Gamma$ be a left-covariant first order differential *-calculus over A such that $\Gamma$ is self-dual and invariant under the Hopf algebra automorphism S^2. A quantum Clifford…

We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new computational method that yields a streamlined computation of the first 61 stable homotopy groups, and gives new information about the stable…

We prove a filtered version of the Homotopy Transfer Theorem which gives an A-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the…

We discover a new example of a generic rank 2-distribution on a 5-manifold with a 6-dimensional transitive symmetry algebra, which is not present in Cartan's classical five variables paper. It corresponds to the Monge equation z' = y +…

We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincar\'e series of the minimal set of generators of the graded algebra of regular functions, provided that the link of the…