arXiv subjects

Nicolas Guès

Publications and source records attributed to Nicolas Guès.

2 recordsLinked to original sources

arXiv2026

Linear stable ranges for integral homotopy groups of configuration spaces

We prove explicit linear stable ranges for the $\mathsf{FI}$-modules $\mathrm{Hom}(π_p \mathrm{Conf} M, \mathbb Z)$ and $\mathrm{Ext}(π_p \mathrm{Conf} M, \mathbb Z)$ with $\mathrm{Conf} M$ being the configuration co$\mathsf{FI}$-space of a $d$-dimensional manifold with $d \geq 3$. The proof of this result uses a homotopy-theoretic approach to representation stability for $\mathsf{FI}$-modules. This allows us to derive representation stability results from homotopy-theoretical statements, in particular the generalized Blakers-Massey theorem. We also generalize to $\mathsf{FI}_G$-modules and orbit configuration spaces.

math.AT↗

arXiv2025

Periodicity in the homology of moduli spaces of disconnected submanifolds

We show that the moduli space of $n$ suitably embedded copies of a closed smooth manifold $P$ inside a closed smooth manifold $M$ satisfies cohomological periodicity over $\mathbb F_\ell$ when $n$ grows, with an explicit linear bound on the period and the periodicity range. This generalizes a known result about configuration spaces. We also show integral stability of the cohomology when $M$ is open, reproving a result of Palmer and improving the slope when inverting $2$. The main input in the proof is Goodwillie and Klein's multiple disjunction lemma for embedding spaces. As a corollary we get stability and periodicity results for some classes of symmetric diffeomorphism groups of manifolds.

math.AT↗