Related papers: Steenrod operations on the modular invariants
Let $p$ be an odd prime and $\mathbb{F}_p$ be the prime field of order $p$. Consider a $2$-dimensional orthogonal group $G$ over $\mathbb{F}_p$ acting on the standard representation $V$ and the dual space $V^*$. We compute the invariant…
We prove necessary and sufficient conditions for the existence of non-trivial Steenrod actions on the mod-$2$ cohomology of 4-dimensional toric orbifolds. As applications, the stable homotopy type and the gauge groups of a $4$-dimensional…
On d\'emontre une conjecture due \`a N. Kuhn concernant la cohomologie singuli\`ere \`a coefficients mod p des espaces, comme module instable sur l'alg\`ebre de Steenrod. Notre d\'emonstration de ce r\'esultat, d\'ej\`a connu en…
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…
The study of the action of the Steenrod algebra on the mod $p$ cohomology of spaces has many applications to the topological structure of those spaces. In this paper we present combinatorial formulas for the action of Steenrod operations on…
The Cartan formula relates the cup product and the action of the Steenrod algebra on mod~$p$ cohomology. For any pair of mod $p$ cocycles in a simplicial set, where $p$ is an odd prime, we effectively construct a natural coboundary…
Steenrod operations have been defined by Voedvodsky in motivic cohomology in order to show the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper is to provide…
We describe the action of the mod $2$ Steenrod algebra on the cohomology of various polyhedral products and related spaces. We carry this out for Davis-Januszkiewicz spaces and their generalizations, for moment-angle complexes as well as…
In this paper we use Peter May's algebraic approach to Steenrod operations to construct Steenrod's reduced power operations in simplicial Bredon-Illman cohomology with local coefficients of a one vertex G-Kan complex, G being a discrete…
On d\'emontre une conjecture due \'a N. Kuhn concernant la cohomologie singuli\'ere \'a coefficients mod p des espaces, comme module instable sur l'alg\'ebre de Steenrod. Notre d\'emonstration de ce r\'esultat, d\'ej\'a connu en…
We show that operations in Milnor K-theory mod $p$ of a field are spanned by divided power operations. After giving an explicit formula for divided power operations and extending them to some new cases, we determine for all fields $k$ and…
When a cyclic group G of prime order acts on a 4-manifold X, we prove a formula which relates the Seiberg-Witten invariants of X to those of X/G.
Based on a relative Wu theorem in \'etale cohomology, we study the compatibility of Steenrod operations on Chow groups and on \'etale cohomology. Using the resulting obstructions to algebraicity, we construct new examples of non-algebraic…
The classical Schubert cells on a flag manifold G/H give a cell decomposition for G/H whose Kronecker duals (known as Schubert classes) form an additive base for the integral cohomology H^{\ast}(G/H). We present a formula that expresses…
We introduce a new model for the secondary Steenrod algebra at the prime 2 which is both smaller and more accessible than the original construction of H.-J. Baues. We also explain how BP can be used to define a variant of the secondary…
We investigate the mod $p$ Buchstaber invariant of the skeleta of simplices, for a prime number $p$, and compare them for different values of $p$. For $p=2$, the invariant is the real Buchstaber invariant. Our findings reveal that these…
We explore in this paper the spaces of common zeros of several deformations of Steenrod operators.
In the paper "The Steenrod algebra and its dual", J.Milnor determined the structure of the dual Steenrod algebra which is a graded commutative Hopf algebra of finite type. We consider the affine group scheme $G_p$ represented by the dual…
Let $p$ be a prime number, $p=2^nq+1$, where $q$ is odd. D. Shanks described an algorithm to compute square roots $\pmod{p}$ which needs $O(\log q + n^2)$ modular multiplications. In this note we describe two modifications of this…
Working over the prime field F_p, the structure of the indecomposables Q^* for the action of the algebra of Steenrod reduced powers A(p) on the symmetric power functors S^* is studied by exploiting the theory of strict polynomial functors.…