arXiv subjects

Coline Emprin

Publications and source records attributed to Coline Emprin.

5 recordsLinked to original sources

arXiv2025

Obstruction sequences to homotopy equivalences

We develop an obstruction theory for the existence of gauge equivalences in complete differential graded Lie algebras. Specifically, this theory provides a characterization of homotopy equivalences between differential graded algebras governed by operads or properads, potentially colored in a groupoid. We apply this framework to establish new homotopy equivalence results in both algebraic topology and algebraic geometry, with a particular focus on the study of minimal models for highly connected varieties.

math.AT↗

arXiv2025

Properadic coformality of spheres

We define a properad $Y^{(n)}_\infty$ that encodes $n$-pre-Calabi--Yau algebras with vanishing copairing. These algebras include chains on the based loop space of any space $X$ endowed with a fundamental class $[X]$ such that $(X,[X])$ satisfies Poincar\'e duality of degree $n \geqslant 1$ with local system coefficients, such as an oriented manifold. Extending the notion of coformality of spaces, we define coformality of such a pair $(X,[X])$ in terms of properadic formality of $Y^{(n)}_\infty$-algebra structures on $C_*(\Omega X)$. Using a refined version of properadic Kaledin classes, we establish the intrinsic coformality of all spheres in characteristic zero.

math.AT↗

arXiv2024

Weight structures and formality

This is a survey on formality results relying on weight structures. A weight structure is a naturally occurring grading on certain differential graded algebras. If this weight satisfies a purity property, one can deduce formality. Algebraic geometry provides us with such weight structures as the cohomology of algebraic varieties tends to present additional structures including a Hodge structure or a Galois action.

math.AT↗

arXiv2024

Kaledin classes and formality criteria

We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded algebras over operads or properads, possibly colored in groupoids. The present treatment generalizes the previous obstruction classes in two directions: outside characteristic zero and including a wider range of algebraic structures. This enables us to establish novel formality criteria, including formality descent with torsion coefficients, formality in families, intrinsic formality, and criteria in terms of chain-level lifts of homology automorphism.

math.AT↗

arXiv2024

A prop structure on partitions

Motivated by its link with functor homology, we study the prop freely generated by the operadic suspension of the operad Com. We exhibit a particular family of generators, for which the composition and the symmetric group actions admit simple descriptions. We highlight associated subcategories of its Karoubi envelope which allows us to compute extensions groups between simple functors from free groups. We construct a particular prop structure on partitions whose composition corresponds to the Yoneda product of extensions between exterior power functors.

math.AT↗