相关论文: Stability conditions on triangulated categories
We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually…
We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…
Using the generalised AdS/CFT correspondence, we show that there are certain ten-dimensional differentiable manifolds such that string theory on such a manifold is unstable [to the emission of "large branes"] no matter what the metric may…
We discuss how stability is related to the D-topology of mapping spaces, equipped with the functional diffeology. Indeed, we show that stable classes of mapping spaces are D-open. After a reformulation of the classical stability theorem of…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
We present a notion of $\Delta$-stability and stability filtration in arbitrary categories which is equivalent to the existence of Harder-Narasimhan (HN) sequences on objects. Indeed it is equivalent to the existence of a zero morphism, a…
We present a simple model for the late time stabilization of extra dimensions. The basic idea is that brane solutions wrapped around extra dimensions, which is allowed by string theory, will resist expansion due to their winding mode. The…
In this paper we show how the existence of a certain stable cylinder determines (locally) the ambient manifold where it is immersed. This cylinder has to verify a {\it bifurcation phenomena}, we make this explicit in the introduction. In…
We give a brief introduction to the relationship between Bridgeland stability conditions and the $K(\pi,1)$ conjecture for Artin groups. These notes have been written as pre-reading for the MFO mini-workshop 2405a: Artin groups meet…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas…
In this paper, we give a definition of weak stability condition on a triangulated category. The difference between our definition and existing definitions is that we allow objects in the kernel to have non-maximal phases. We then construct…
We use the model of L. Randall et al to investigate the stability of allowed quantum field configurations. Firstly, we find that due to the topology of this 5 dimensional model, there are 2 possible configurations of the scalar field,…
As shown by Happel, from any Frobenius exact category, we can construct a triangulated category as a stable category. On the other hand, it was shown by Iyama and Yoshino that if a pair of subcategories $\mathcal{D}\subseteq\mathcal{Z}$ in…
We study a stabilization of the symplectic category introduced by A. Weinstein as a domain for the geometric quantization functor. The symplectic category is a topological category with objects given by symplectic manifolds, and morphisms…
We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
We begin by discussing various ways autoequivalences and stability conditions associated to triangulated categories can interact. Once an appropriate definition of compatibility is formulated, we derive a sufficiency criterion for this…
We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…
In this letter, a new notion of stability is introduced, which is called triangular stability. A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its…