Related papers: The stabilization theorem for proper groupoids

We develop a mechanism of "isotropy separation for compact objects" that explicitly describes an invertible $G$-spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module…

The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…

Given a set of prime numbers S, we localise equivariant bivariant Kasparov theory at S and compare this localisation with Kasparov theory by an exact sequence. More precisely, we define the localisation at S to be KK^G(A,B) tensored with…

We consider functors from the category of locally convex algebras to abelian groups and prove invariance under smooth homotopies for weakly J-stable algebras, where J is a harmonic operator ideal. This applies in particular to negative…

We study the stabiliser formalism for qudits of arbitrary dimension $d$. In the free case, we show that the basic theorem of the stabiliser formalism remains valid: if the stabiliser subgroup $H$ is free as a $Z/dZ$-module and contains no…

Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which…

In this paper, by introducing a wider class of one-parameter group actions for test configurations, we have a stronger form of the definition of K-stability. This allows us to obtain some key step of my preceding work in proving that…

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…

Let $G$ be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of $G$ on $C^*$-algebras $A$ and $B$ are outer conjugate if and only if there is an isomorphism of the crossed products that is…

Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifold M, with compact quotient. There is an assembly map which associates to any G-equivariant K-homology class on M, an element of the…

We introduce a notion of local Hilbert--Schmidt stability, motivated by the recent definition by Bradford of local permutation stability, and give examples of (non-residually finite) groups that are locally Hilbert--Schmidt stable but not…

Let $N$ be a normal subgroup of a group $G$. An $N$-module $Q$ is $G$-stable provided that $Q$ is equivalent to the twist $Q^g$ of $Q$ by $g$, for every $g\in G$. If the action of $N$ on $Q$ extends to an action of $G$ on $Q$, $Q$ is…

The classical trace map is a highly non-trivial map from algebraic K-theory to topological Hochschild homology (or topological cyclic homology) introduced by B\"okstedt, Hsiang and Madsen. It led to many computations of algebraic K-theory…

We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and…

We define equivariant projective unitary stable bundles as the appropriate twists when defining K-theory as sections of bundles with fibers the space of Fredholm operators over a Hilbert space. We construct universal equivariant projective…

In this paper, we prove the Novikov conjecture for a class of highly non-linear groups, namely discrete subgroups of the diffeomorphism group of a compact smooth manifold. This removes the volume-preserving condition in a previous work.…

In this paper we develop a theory of stability for $G$-categories (presheaf of categories on the orbit category of $G$), where $G$ is a finite group. We give a description of Mackey functors as $G$-commutative monoids exploit it to…

In a previous paper, arXiv:1301.4409, we showed that the moduli space of curves C with a G-symmetry (that is, with a faithful action of a finite group G), having a fixed generalized homological invariant, is irreducible if the genus g' of…

We develop equivariant KK-theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce…