Tootfinder

This https://arxiv.org/abs/2301.02491 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids
We first revisit the construction of Quinn's finite total homotopy TQFT, which depends on the choice of a homotopy finite space, $\boldsymbol{B}$. This constitutes a vast generalisation of the Dijkgraaf-Witten TQFT, with a trivial cocycle, and of Yetter's homotopy 2-type TQFT. We build our construction directly from homotopy theoretical techniques, and hence, as in Quinn's original notes from 1995, the construction works in all dimensions. Our aim in this is to provide background for giving i…

Column | Ongehoorde politieke aanval op Europees hof – op het slechtst denkbare moment - @… - #NRC

Da ist gerade ein handflächengroßer #Hirschkäfer gegen unser Wohnzimmerfenster geflogen und hat sich leider/zum Glück so schnell wieder aufgerappelt, dass er mit Davonfliegen schneller war als ich mit der Kamera XD
#Darmstadt

Higher homotopy wild sets
Jeremy Brazas, Atish Mitra
https://arxiv.org/abs/2505.23665 https://arxiv.org/pdf/2505.23665

Higher homotopy wild sets
The $π_n$-wild set $\mathbf{w}_{n}(X)$ of a topological space $X$ is the subspace of $X$ consisting of the points at which there exists a shrinking sequence of essential based maps $S^n\to X$. In this paper, we show that the homotopy type of $\mathbf{w}_{n}(X)$ is a homotopy invariant of $X$ and, in analogy to the known one-dimensional case, we show that for certain $n$-dimensional $π_n$-shape injective metric spaces, the homeomorphism type of $\mathbf{w}_{n}(X)$ is a homotopy invariant of $X…

Wie handfest ist die angekündigte Hilfe?
Der Besuch des ukrainischen Präsidenten im Kanzleramt stand ganz im Zeichen der Waffenhilfe. Deutschland sendet ein Signal der Unterstützung - doch wie handfest ist die angekündigte Hilfe?
🔗 https://www.tagessch…

Was vom Besuch Selenskyjs in Berlin bleibt
Der Besuch des ukrainischen Präsidenten im Kanzleramt stand ganz im Zeichen der Waffenhilfe. Deutschland sendet ein Signal der Unterstützung - doch wie handfest ist die angekündigte Hilfe?

Simplicial methods in the resource theory of contextuality
Aziz Kharoof, Cihan Okay
https://arxiv.org/abs/2505.24010 https://arxiv.or…

Simplicial methods in the resource theory of contextuality
We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on the theory of simplicial distributions, which integrates homotopy-theoretic structures with probability, we introduce event scenarios as a functorial generalization of presheaf-theoretic measurement scenarios and prove their equivalence to bundle scenarios via the Grothendieck construction. We define symmetric monoidal …

A Homotopical Invariant of Weinstein Surfaces
Shanon J. Rubin
https://arxiv.org/abs/2505.23377 https://arxiv.org/pdf/2505.23377

A Homotopical Invariant of Weinstein Surfaces
One generally expects that the techniques of arboreal singularities and gluing of local differential graded categories will result in a useful global invariant for all Weinstein manifolds. In this paper we construct explicit models for the homotopy limits of diagrams of microlocal sheaf categories which arise from Weinstein surfaces with arboreal skeleta. This is done by characterizing all relevant Reedy model structures on the categories of diagrams that we care about. We prove invariance usin…

A modern perspective on rational homotopy theory
Eleftherios Chatzitheodoridis
https://arxiv.org/abs/2505.23322 https://arxiv.org/pdf…

A modern perspective on rational homotopy theory
In Quillen's paper on rational homotopy theory, the category of 1-reduced simplicial sets is endowed with a family of model structures, the most prominent of which is the one whose weak equivalences are the rational homotopy equivalences. In this paper, we give a modern approach to this family of model structures.

This https://arxiv.org/abs/2411.03277 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotic stability equals exponential stability -- while you twist your eyes
Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this homotopy.

Simplicial properadic homotopy
Eric Hoffbeck, Johan Leray, Bruno Vallette
https://arxiv.org/abs/2505.22004 https://arxiv.org/pdf/2505…

Simplicial properadic homotopy
In this paper, we settle the homotopy properties of the infinity-morphisms of homotopy (bial)-gebras over properads, i.e. algebraic structures made up of operations with several inputs and outputs. We start by providing the literature with characterizations for the various types of infinity-morphisms, the most seminal one being the equivalence between infinity-quasi-isomorphisms and zig-zags of quasi-isomorphisms which plays a key role in the study the formality property. We establish a simplic…