Paul-Eugène Parent

activity

20042026

most citedA canonical enriched Adams-Hilton model for simplicial sets

23 citations · 36 across the 9 of their papers we have counts for

collaborators

12 papers

math.AT2026

Poincaré duality and module topological complexity

Paul-Eugène Parent

Topological complexity, introduced by Farber, measures the number of continuous local motion-planning rules on a configuration space. For every simply connected space $X$ of finite…

math.AT2026

Sectional category versus module sectional category for retractive maps

Paul-Eugene Parent

We construct a map between simply connected rational spaces of finite rational type which admits a homotopy retraction and satisfies $m sec a t (p) = 2 < sec a t (p) = 3$ . The target is the rat…

math.AT2026

Homotopical Nilpotency and Homology Nilpotency: A Dimension--Connectivity Bound

Paul-Eugene Parent

Let $X$ be a $(q - 1)$ -connected rational space of finite type, where $q \geq 2$ , with homotopical nilpotency $ni l_{h} (X) = n \geq 1$ . If $H^{> N} (X; Q) = 0$ and $N \leq q (n + 3) - 3$ , we prove that $Hn…

math.AT2026

Homology Nilpotency in Rational Homotopy Theory: Cell Attachments, Retractive Towers, Divergence, and Stabilization

Paul-Eugène Parent

Homology nilpotency of a simply connected minimal Sullivan algebra $M$ is the least integer $n$ for which $(M^{+})^{n + 1}$ is contained in an acyclic differential ideal. We develop lo…

math.AT2025

Cone length and Lusternik-Schnirelmann category in rational homotopy

Paul-Eugène Parent, Daniel Tanré

Lusternik-Schnirelmann category (LS-category) of a topological space is the least integer $n$ such that there is a covering of $X$ by $n + 1$ open sets, each of them being contractib…

math.AT2016★ 1 cited

Module sectional category of products

J. G. Carrasquel-Vera, P. -E. Parent, L. Vandembroucq

Extending a result of Félix-Halperin-Lemaire on Lusternik-Schnirelmann category of products, we prove additivity of a rational approximation for Schwarz's sectional category with r…