Related papers: The Action by Natural Transformations of a Group o…

Symbolic dynamics is partly the study of walks in a directed graph. By a walk, here we mean a morphism to the graph from the Cayley graph of the monoid of non-negative integers. Sets of these walks are also important in other areas, such as…

G-equivariant modular categories provide the input for a standard method to construct 3d homotopy field theories. Virelizier constructed a G-equivariant category from the action of a group G on a Hopf algebra H by Hopf algebra…

We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show…

Let M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M,boundary of M) can be recovered from the configuration category of the interior of M. The grouplike monoid of…

Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions). In this paper we expand the existing framework, so that it will apply to not…

Let $\Delta$ be a foliation on a topological manifold $X$, $Y$ be the space of leaves, and $p: X \to Y$ be the natural projection. Endow $Y$ with the factor topology with respect to $p$. Then the group $\mathcal{H}(X, \Delta)$ of foliated…

Every action of a finite group scheme $G$ on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of $G$-normalization. In particular, every curve equipped with…

For an arbitrary localic etale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of G-actions is…

An orbifold is a topological space modeled on quotient spaces of a finite group actions. We can define the universal cover of an orbifold and the fundamental group as the deck transformation group. Let $G$ be a Lie group acting on a space…

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…

The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…

We study higher analogues of effective and effectual topological complexity of spaces equipped with a group action. These are $G$-homotopy invariant and are motivated by the (higher) motion planning problem of $G$-spaces for which their…

We show that if a (locally compact) group $G$ acts properly on a locally compact $\sigma$-compact space $X$ then there is a family of $G$-invariant proper continuous finite-valued pseudometrics which induces the topology of $X$. If $X$ is…

The paper constructs the analytic index for an elliptic pseudodifferential family of $L^{m}_{\rho,\de}$-operators invariant under the proper action of a continuous family groupoid on a $G$-compact, $C^{\infty,0}$ $G$-space.

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category $\mathsf{C}$ of groups with operations using the categorical equivalence between crossed modules and internal categories in…

Some well-known and less well-known or new notions related to group actions are surveyed. Some of these notions are used to generalize affine spaces. Actions are seen as functions with values in transformation monoids

This article explores the novel notion of gyrogroup actions, which is a natural generalization of the usual notion of group actions. As a first step toward the study of gyrogroup actions from the algebraic viewpoint, we prove three…

In this paper, we study equivariant real cycle class maps for group actions on real schemes, with a view toward Witt-sheaf characteristic classes. The cycle class maps take values in singular cohomology of the real points of the quotient…

In this paper author proposes a construction of a universal space of type $K(\pi,1)$ such that any action (up to homotopy conjugation) of a given finite group $G$ on spaces of the same homotopy type is presented on the constructed space.…

We define homotopy group actions in terms of families of $A_\infty$ algebras indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism induced by a path on the manifold and for the $A_\infty$ homotopy corresponding to a…