v1-periodic homotopy groups of the Dwyer-Wilkerson space

Let $P_q$ be the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_q]$ over the prime field of two elements, $\mathbb F_2$, with the degree of each $x_i$ being 1. We study the {\it hit Peterson problem} of finding a minimal set of generators for $P_q$ as a module over the mod-$2$ Steenrod algebra, $\mathcal{A}.$ In this note, we present the minimal sets of $\mathcal{A}$-generators for $P_5$ in the cases where the degree are sufficiently general.

math.AT↗

arXiv2026

Homotopy lifting property in symmetric products

In this paper we prove the homotopy lifting property for symmetric products $SP_{m}(X)$ and $F_{m}(X)$, with $X$ a Hausdorff topological space. Furthermore, we introduce a new tool, the theory of topological puzzles, to get a useful decomposition of $X^{m}$.

math.AT↗

arXiv2026

Homotopy lifting property for actions of finite abelian groups on Hausdorff topological spaces

In this paper we prove the homotopy lifting property for actions of finite abelian groups on Hausdorff topological spaces.

math.AT↗