Related papers: Sheaves of G-structures and generic G-models

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex…

An attempt is made to bring into harmony two of the paradigms commonly used in the theory of continuous distributions of defects. It is shown that the common differential geometric apparatus is provided neatly by the theory of G-structures.…

We give explicit axioms for the algebraic theory of the quasivarieties of right-preordered groups and preordered groups. We then look at lattices of effective equivalence relations, which turn out to be similar to the lattices of…

In this paper we introduce an intrinsic version of the classical induction of representations for a subgroup $H$ of a (finite) group $G$, called here {\em geometric induction}, which associates to any, not necessarily transitive, $G$-set…

For any finite group G with a finite G-set X and a modular tensor category C we construct a part of the algebraic structure of an associated G-equivariant monoidal category: For any group element g in G we exhibit the module category…

We show that for any clopen collection X of subgroups of G with finite Weyl groups, the category of G-spectra with geometric isotropy in X is equivalent to the category of equivariant sheaves over X. This gives an algebraic model of…

For every stable model category $\mathcal{M}$ with a certain extra structure, we produce an associated model structure on the pro-category pro-$\mathcal{M}$ and a spectral sequence, analogous to the Atiyah-Hirzebruch spectral sequence, with…

For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor,…

If $X$ is a variety with an additional structure $\xi$, such as a marked point, a divisor, a polarization, a group structure and so forth, then it is possible to study whether the pair $(X,\xi)$ is defined over the field of moduli. There…

An isovariant map between spaces with a group action is an equivariant map which preserves isotropy groups. In this paper, we show that for a finite group $G$, the category of $G$-spaces with isovariant maps has a Quillen model structure.…

In this paper, using the quantum McKay correspondence, we construct the "derived category" of G-equivariant sheaves on the quantum projective line at a root of unity. More precisely, we use the representation theory of U_{q}sl(2) at root of…

Let $G\subset GL(V)$ be a linear Lie group with Lie algebra $\frak g$ and let $A(\frak g)^G$ be the subalgebra of $G$-invariant elements of the associative supercommutative algebra $A(\frak g)= S(\frak g^*)\otimes \La(V^*)$. To any…

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…

In this paper, we introduce a method to construct new categories which look like "cubes", and discuss model structures on the presheaf categories over them. First, we introduce a notion of thin-powered structure on small categories, which…

We investigate group actions on the category of coherent sheaves over weighted projective lines. We show that the equivariant category with respect to certain finite group action is equivalent to the category of coherent sheaves over a…

Let $k_0$ be a field of characteristic $0$ with algebraic closure $k$. Let $G$ be a connected reductive $k$-group, and let $Y$ be a spherical variety over $k$ (a spherical homogeneous space or a spherical embedding). Let $G_0$ be a…

There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

An equivariant topological field theory is defined on a cobordism category of manifolds with principal fiber bundles for a fixed (finite) structure group. We provide a geometric construction which for any given morphism $G \to H$ of finite…

Drawing inspiration from the achievements of natural language processing, we adopt self-supervised learning and utilize an equivariant graph neural network to develop a unified platform designed for training generative models capable of…