Related papers: Infinity-operadic foundations for embedding calcul…
We continue developing the theory around the twin-width of totally ordered binary structures, initiated in the previous paper of the series. We first introduce the notion of parity and linear minors of a matrix, which consists of…
We give a framework for comparing on the one hand theories of n-categories that are weakly enriched operadically, and on the other hand n-categories given as algebras for a contractible globular operad. Examples of the former are the…
For an integer $r\ge 2$, the space of $r$-immersions of $M$ in $\R^n$ is defined to be the space of immersions of $M$ in $\R^n$ such that at most $r-1$ points of $M$ are mapped to the same point in $\R^n$. The space of $r$-immersions lies…
For topologically mixing locally conformal semigroup actions generated by a finite collection of $C^{1+\alpha}$ conformal local diffeomorphisms, we provide a countable Markov partition satisfying the finite images and the finite cycle…
We show that embedding calculus invariants $ev_n$ are surjective for long knots in an arbitrary $3$-manifold. This solves some remaining open cases of Goodwillie--Klein--Weiss connectivity estimates, and at the same time confirms one half…
We build new algebraic structures, which we call genuine equivariant operads, which can be thought of as a hybrid between equivariant operads and coefficient systems. We then prove an Elmendorf-Piacenza type theorem stating that equivariant…
We show that Koszul duality for operads in $(\mathrm{Top},\times)$ can be expressed via generalized Thom complexes. As an application, we prove the Koszul self duality of the little disk modules $E_M$. We discuss implications for…
We show that in codimension at least 3, spaces of locally flat topological embeddings of manifolds are correctly modelled by derived spaces of maps between their configuration categories (under mild smoothability conditions). That general…
In this paper we study duoidal structures on $\infty$-categories of operadic modules. Let $\mathcal{O}^{\otimes}$ be a small coherent $\infty$-operad and let $\mathcal{P}^{\otimes}$ be an $\infty$-operad. If a…
The structure of a $k$-fold monoidal category as introduced by Balteanu, Fiedorowicz, Schw\"anzl and Vogt can be seen as a weaker structure than a symmetric or even braided monoidal category. In this paper we show that it is still…
The embedding theorem of Roelcke and Dierolf for the completions of four standard uniform structures on topological groups and their quotients holds more generally for spaces of uniform measures. The natural mappings between the four spaces…
We give elements towards the classification of quantum Airy structures based on the $W(\mathfrak{gl}_r)$-algebras at self-dual level based on twisted modules of the Heisenberg VOA of $\mathfrak{gl}_r$ for twists by arbitrary elements of the…
Starting from any operad P, one can consider on one hand the free operad on P, and on the other hand the Baez--Dolan construction on P. These two new operads have the same space of operations, but with very different notions of arity and…
This work addresses the homotopical analysis of enveloping operads in a general cofibrantly generated symmetric monoidal model category. We show the potential of this analysis by obtaining, in a uniform way, several central results…
An influential result of McDuff and Schlenk asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a remarkable structure: the function has infinitely many…
We study categorial properties of the operadic twisting functor Tw. In particular, we show that Tw is a comonad. Coalgebras of this comonad are operads for which a natural notion of twisting by Maurer-Cartan elements exists. We give a large…
In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad $\{\bar{M}_{0,n+1}\}$ can be endowed with natural descent data that allow it to be considered as the lift to ${\rm Spec}\,\Z$ of an…
A central question in equivariant algebraic K-theory asks whether there exists an equivariant K-theory machine from genuine symmetric monoidal G-categories to orthogonal G-spectra that preserves equivariant algebraic structures. We answer…
Concrete two-set (module-like and algebra-like) algebraic structures are investigated from the viewpoint that the initial arities of all operations are arbitrary. Relations between operations arising from the structure definitions, however,…
Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…