Tootfinder

From homotopy Rota-Baxter algebras to Pre-Calabi-Yau and homotopy double Poisson algebras
Yufei Qin, Kai Wang
https://arxiv.org/abs/2506.03952 https://

From homotopy Rota-Baxter algebras to Pre-Calabi-Yau and homotopy double Poisson algebras
In this paper, we investigate pre-Calabi-Yau algebras and homotopy double Poisson algebras arising from homotopy Rota-Baxter structures. We introduce the notion of cyclic homotopy Rota-Baxter algebras, a class of homotopy Rota-Baxter algebras endowed with additional cyclic symmetry, and present a construction of such structures via a process called cyclic completion. We further introduce the concept of interactive pairs, consisting of two differential graded algebras-designated as the acting al…

Existence of infinitely many homotopy classes from $\mathbb S^3$ to $\mathbb S^2$ having a minimimzing $W^{s,\frac 3s}$-harmonic map
Adam Grzela, Katarzyna Mazowiecka
https://arxiv.org/abs/2506.05060

Existence of infinitely many homotopy classes from $\mathbb S^3$ to $\mathbb S^2$ having a minimimzing $W^{s,\frac 3s}$-harmonic map
In 1998 T. Rivière proved that there exist infinitely many homotopy classes of $π_3(\mathbb S^2)$ having a minimizing 3-harmonic map. This result is especially surprising taking into account that in $π_3(\mathbb S^3)$ there are only three homotopy classes (corresponding to the degrees $\{-1,0,1\}$) in which a minimizer exists. We extend this theorem in the framework of fractional harmonic maps and prove that for $s\in(0,1)$ there exist infinitely many homotopy classes of $π_{3}(\mathbb S^…

Equivariant deformation problems and homotopy operators
Sebasti\'an Daza, Jo\~ao Nuno Mestre
https://arxiv.org/abs/2506.03967 https://

Equivariant deformation problems and homotopy operators
We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and explicit proofs of rigidity and unobstructedness theorems.

@… Fred Meyer out here in Battle Ground had a handful when I was just there. And no long lines either.

Is Crane--Yetter fully extended?
Luuk Stehouwer
https://arxiv.org/abs/2506.04864 https://arxiv.org/pdf/2506.04864

Is Crane--Yetter fully extended?
We revisit the question of whether the Crane-Yetter topological quantum field theory (TQFT) associated to a modular tensor category admits a fully extended refinement. More specifically, we use tools from stable homotopy theory to classify extensions of invertible four-dimensional TQFTs to theories valued in symmetric monoidal 4-categories whose Picard spectrum has nontrivial homotopy only in degrees 0 and 4. We show that such extensions are classified by two pieces of data: an equivalence clas…

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This https://arxiv.org/abs/2412.04116 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Polyhedral products associated to pseudomanifolds
We study the homotopy theory of polyhedral products associated to a combinatorial generalisation of manifolds known as pseudomanifolds. As special cases, we show that loop spaces of moment-angle manifolds associated to triangulations of $S^2$ and $S^3$ decompose as a product of spheres and loops on spheres.

Designing Algorithmic Delegates: The Role of Indistinguishability in Human-AI Handoff
Sophie Greenwood, Karen Levy, Solon Barocas, Hoda Heidari, Jon Kleinberg
https://arxiv.org/abs/2506.03102

Designing Algorithmic Delegates: The Role of Indistinguishability in Human-AI Handoff
As AI technologies improve, people are increasingly willing to delegate tasks to AI agents. In many cases, the human decision-maker chooses whether to delegate to an AI agent based on properties of the specific instance of the decision-making problem they are facing. Since humans typically lack full awareness of all the factors relevant to this choice for a given decision-making instance, they perform a kind of categorization by treating indistinguishable instances -- those that have the same o…

This https://arxiv.org/abs/2406.18497 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The equivariant model structure on cartesian cubical sets
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved Eilenberg-Zilber category. The key innovation is an additional equivariance condition in the specification of the cubical Kan fibrations, which can be described as the pullback of an interval-based class of uniform fibrations in the category of symmetric sequences of cu…

This https://arxiv.org/abs/2405.19258 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Polyhedral coproducts
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral coproducts, surveying the Eckmann-Hilton duals of various familiar examples and properties of polyhedral products. In particular, we show that polyhedral coproducts give a functorial interpolation between the wedge and cartesian product of spaces which differs from the…