Phúc Võ Dang

activity

20152026

most citedOn a minimal set of generators for the polynomial algebra of five variables as a module over the Steenrod algebra

55 citations · 103 across the 26 of their papers we have counts for

collaborators

27 papers

math.AT2026

Binary Minor Certificates for the $A (1)$ -hit problem of $M O (2)$

Dang Vo Phuc

Let $M = H^{*} (M O (2); F_{2})$ and let $A (1)$ be the subalgebra of the mod $2$ Steenrod algebra generated by $Sq^{1}$ and $Sq^{2}$ . In…

math.AT2026

Two-Sided Dimension Bounds for the Peterson Hit Problem via Projections and Matrix Minors

Dang Vo Phuc, Peter V. Danchev

Let $P_{k} = F_{2} [x_{1}, \dots, x_{k}]$ be the polynomial algebra over the prime field $F_{2}$ , viewed as an unstable module over the mod- $2$ Steenrod algebra $\mathca…

math.AT2026

The Symmetric Hit Problem in Four Variables: Relative Cohits and Stabilizer-Fixed Preimages

Dang Vo Phuc, Peter V. Danchev

In this work, we study the symmetric hit problem in four variables by analyzing the relative cohit space, defined as the kernel of the inclusion-induced map from symmetric to ordin…

math.AT2026

The rank-five Peterson hit problem, the fifth Singer transfer, and a geometric generator in unoriented cobordism

Dang Vo Phuc

The Peterson hit problem seeks a minimal set of generators for the polynomial algebra $P_{s} = F_{2} [x_{1}, \dots, x_{s}]$ as an unstable module over the mod-2 Steenrod algebra $\ma…

math.AT2026

A Note on the 2-Local Homotopy Types of $G_{2}$ -Gauge Groups

Dang Vo Phuc

In a recent preprint \cite{Kameko2026} , Kameko presented a substantial completion of the 2-local classification of $G_{2}$ -gauge groups over $S^{4}$ , extending earlier work by Kishimo…

math.AT2026

Adams filtrations and secondary coherence for fibers of Steenrod operations

Dang Vo Phuc

Let $f : Y \to \prod_{λ} Σ^{d_{λ}} H F_{2}$ be a locally finite family of positive-degree stable operations, where $Y = H F_{2}$ or $H Z$ ; in the integral case assume $d_λ\geq…

math.AT2026

Local Parity and Systematic Peterson Counterexamples in the Motivic Hit Problem

Dang Vo Phuc

The motivic hit problem asks for a minimal set of module generators of $H^{*, *} (B V_{n}; F_{2})$ over the mod~ $2$ motivic Steenrod algebra. Kameko proved that the motivic Peterso…

math.AT2026

The fifth algebraic transfer in generic degrees and validation of a localized Kameko's conjecture

Dang Vo Phuc

This paper develops our previous works concerning the classical Peterson hit problem for the polynomial algebra on five variables over the mod--2 Steenrod algebra $A$ in a…

math.AT2025

Low-degree mod 2 cohomology of classifying spaces of $G_{2}$ -gauge groups

Dang Vo Phuc

Let $G_{k}$ denote the gauge group of the principal $G_{2}$ --bundle over $S^{4}$ classified by $k \in π_{4} (B G_{2}) ≅ Z$ . Motivated by the $p$ --local homotopy classificat…

math.RT2025

Spectral Separation and Eigenvalue Labelling for Polynomial Tensor Representations of General Linear Groups

Dang Vo Phuc

Let $q = p^{f}$ be a prime power, $H \leq GL_{d} (q)$ a subgroup containing a genuine Singer cycle $s$ of order $q^{d} - 1$ , and $W$ an $F_{q} H$ -module whose scalar extension…

math.AT2025

The rank-five Peterson hit problem, the Singer transfer, and canonical Milnor-operation layers

Dang Vo Phuc

Let $V_{n} = (F_{2})^{n}$ , let $P_{n} = H^{*} (B V_{n}; F_{2}) = F_{2} [u_{1}, \dots, u_{n}]$ , and regard $P_{n}$ as an unstable module over the mod $2$ Steenrod algebra $A$ . We stu…

math.GR2025★ 1 cited

Jensen's Functional Equation on Involution-Generated Groups: A Square-Root Criterion, Rigidity Phenomena, and Obstruction Spaces

Dang Vo Phuc

Let $G$ be a group and $H$ an abelian group. We study normalized solutions $f : G \to H$ of the Jensen equation $f (x y) + f (x y^{- 1}) = 2 f (x)$ and its companion $f (x y) + f (x^{- 1} y) = 2 f (y)$ . Re…

math.AC2025

On modular invariants of the truncated polynomial ring in rank four

Dang Vo Phuc

We prove the rank-4 case of the conjecture of Ha-Hai-Nghia for the invariant subspace of the truncated polynomial ring $\mathcal{Q}_m(n)=\mathbb{F}_q[x_1,\dots,x_n]/(x_1^{q^m},\dot…

math.AC2025

Observation Nuclei in Affine Geometry: Symbolic Powers, Fat Points, and Infinitesimal Recovery

Dang Vo Phuc

This paper integrates point-dependent infinitesimal data into affine geometry through quantale nuclei and finitary weak ideal systems. For a subset $X \subseteq k^{n}$ and a bounded…

math.AT2025

Geometric realization via unoriented bordism and a counterexample to Singer's conjecture for the sixth algebraic transfer

Dang Vo Phuc

Let $A$ be the mod-2 Steenrod algebra acting in the usual way on $P_{q} = F_{2} [x_{1}, \dots, x_{q}]$ , and let $Q P_{q} = F_{2} \otimes_{A} P_{q}$ . Singer's…

math.AT2025

Normalized Derivations for Steenrod--Milnor Operations on the Dickson Algebra and Applications

Dang Vo Phuc

Computing higher iterates of the primitive Steenrod-Milnor operations $St^{\emptyset, Δ_{i}}$ on the Dickson algebra $D_{n}$ has historically been obstructed by severe combinat…

math.AT2025

Computing Invariant Spaces via Global Cluster Analysis and Representation Theory

Dang Vo Phuc

The Singer algebraic transfer is a fundamental homomorphism in algebraic topology, providing a bridge between the homology of classifying spaces and the cohomology of the Steenrod…

math.AT2025

A matrix criterion and algorithmic approach for the Peterson hit problem: Part I

Dang Vo Phuc

The Peterson hit problem in algebraic topology is to explicitly determine the dimension of the quotient space $Q P_{k} = F_{2} \otimes_{A} P_{k}$ in posit…

math.AT2025

On the computation of $Ext_{A}^{k, k +*} (Z /2, Z /2)$ for $k \leq 5$

Dang Vo Phuc

This Note presents a computational algorithm for determining a basis of the cohomology of the mod 2 Steenrod algebra, $\mathrm{Ext}_{\mathcal A}^{k, k+*}(\mathbb{Z}/2, \mathbb{Z}/2…

math.AT2024

On the mod-2 cohomology of the product of the infinite lens space and the space of invariants in a generic degree

Dang Vo Phuc

Let $S^{\infty} / Z_{2}$ be the infinite lens space and $A$ be the Steenrod algebra over the binary field $F_{2} .$ The cohomology $H^{*}((\mathbb S^{\inf…

math.AT2022

On the dimension of the "cohits" space $Z_{2} \otimes_{A_{2}} H^{*} ((R P (\infty))^{\times t}, Z_{2})$ and some applications

Dang Vo Phuc

We denote by $Z_{2}$ the prime field of two elements and by $P_{t} = Z_{2} [x_{1}, \dots, x_{t}]$ the polynomial algebra of $t$ generators $x_{1}, \dots, x_{t}$ with the degree…

math.RA2022★ 42 cited

On the dimension of $H^{*} ((Z_{2})^{\times t}, Z_{2})$ as a module over Steenrod ring

Dang Vo Phuc

We write $P$ for the polynomial algebra in one variable over the finite field $Z_{2}$ and $P^{\otimes t} = Z_{2} [x_{1}, \dots, x_{t}]$ for its $t$ -fold ten…

math.AT2021★ 4 cited

On the lambda algebra and Singer's cohomological transfer

Dang Vo Phuc

Writing $A$ for the 2-primary Steenrod algebra, which is the algebra of stable natural endomorphisms of the mod 2 cohomology functor on topological spaces. Working at the p…

math.AT2021

On modules over the mod 2 Steenrod algebra and hit problems

Dang Vo Phuc

Let us consider the prime field of two elements, $F_{2} \equiv Z_{2} .$ It is well-known that the classical "hit problem" for a module over the mod 2 Steenrod algebra $\m…

Binary Minor Certificates for the A(1)-hit problem of MO(2)

Two-Sided Dimension Bounds for the Peterson Hit Problem via Projections and Matrix Minors

The Symmetric Hit Problem in Four Variables: Relative Cohits and Stabilizer-Fixed Preimages

The rank-five Peterson hit problem, the fifth Singer transfer, and a geometric generator in unoriented cobordism

A Note on the 2-Local Homotopy Types of G2​-Gauge Groups

Adams filtrations and secondary coherence for fibers of Steenrod operations

Local Parity and Systematic Peterson Counterexamples in the Motivic Hit Problem

The fifth algebraic transfer in generic degrees and validation of a localized Kameko's conjecture

Low-degree mod 2 cohomology of classifying spaces of G2​-gauge groups

Spectral Separation and Eigenvalue Labelling for Polynomial Tensor Representations of General Linear Groups

The rank-five Peterson hit problem, the Singer transfer, and canonical Milnor-operation layers

Jensen's Functional Equation on Involution-Generated Groups: A Square-Root Criterion, Rigidity Phenomena, and Obstruction Spaces

On modular invariants of the truncated polynomial ring in rank four

Observation Nuclei in Affine Geometry: Symbolic Powers, Fat Points, and Infinitesimal Recovery

Geometric realization via unoriented bordism and a counterexample to Singer's conjecture for the sixth algebraic transfer

Normalized Derivations for Steenrod--Milnor Operations on the Dickson Algebra and Applications

Computing Invariant Spaces via Global Cluster Analysis and Representation Theory

A matrix criterion and algorithmic approach for the Peterson hit problem: Part I

On the computation of ExtAk,k+∗​(Z/2,Z/2) for k≤5

On the mod-2 cohomology of the product of the infinite lens space and the space of invariants in a generic degree

On the dimension of the "cohits" space Z2​⊗A2​​H∗((RP(∞))×t,Z2​) and some applications

On the dimension of H∗((Z2​)×t,Z2​) as a module over Steenrod ring

On the lambda algebra and Singer's cohomological transfer

On modules over the mod 2 Steenrod algebra and hit problems

Binary Minor Certificates for the $A (1)$ -hit problem of $M O (2)$

A Note on the 2-Local Homotopy Types of $G_{2}$ -Gauge Groups

Low-degree mod 2 cohomology of classifying spaces of $G_{2}$ -gauge groups

On the computation of $Ext_{A}^{k, k +*} (Z /2, Z /2)$ for $k \leq 5$

On the dimension of the "cohits" space $Z_{2} \otimes_{A_{2}} H^{*} ((R P (\infty))^{\times t}, Z_{2})$ and some applications

On the dimension of $H^{*} ((Z_{2})^{\times t}, Z_{2})$ as a module over Steenrod ring