Related papers: $K$-stable splendid Rickard complexes

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover…

Let $n$ be a positive integer and $q$ a prime power. We prove that a refined version of Brou\'{e}'s abelian defect group conjecture holds for unipotent $\ell$-blocks of ${\rm GL}_n(q)$, where $\ell\nmid q$. We also give a sufficient…

Consider the ring $R:=\Q[\tau,\tau^{-1}]$ of Laurent polynomials in the variable $\tau$. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over $R,$ where the action of every standard generator is the multiplication by…

We prove Farber's conjecture on the stable topological complexity of configuration spaces of graphs. The conjecture follows from a general lower bound derived from recent insights into the topological complexity of aspherical spaces. Our…

We show that each block of an alternating group over an arbitrary complete discrete valuation ring is splendidly Rickard equivalent to its Brauer correspondent. This provides new evidence for a refined version of Brou\'{e}'s abelian defect…

In the representation theory of finite groups, there is a well-known and important conjecture, due to Brou\'e saying that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding…

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…

C. Gordon conjectured that a connected sum of two Heegaard splittings is stabilized if and only if one of the two factors is stabilized (Problem 3.91 in Kirby's problem list). In this paper, we shall prove this conjecture.

We give a natural family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe ``wall-crossing behavior'' for objects with the same invariants as $\cO_C(H)$ when H generates Pic(S)…

Let B be a p-block of a finite group G with abelian defect group D such that S\unlhd G, S'=S, G/Z(S)\le\Aut(S) and S/Z(S) is a sporadic simple group. We show that B is isotypic to its Brauer correspondent in N_G(D) in the sense of Brou\'e.…

We describe a procedure to compute the rational nonstable K-groups of A$\mathbb{T}$-algebras. As an application, we show that an A$\mathbb{T}$-algebra is K-stable if and only if it has slow dimension growth.

We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.

We prove K-stability for infinitely many smooth members of the family 2.19 of the Mukai-Mori classification.

The paper investigates the stability properties of restrictions of irreducible representations of the symmetric group to the hyperoctahedral subgroup. A stability result is obtained, analogous to the classical Murnaghan theorem on the…

We give the stable splitting of the complex connective K-theory of the classifying space of special orthogonal groups on even dimensions.

In representation theory of finite groups, there is a well-known and important conjecture due to M. Brou\'e. He conjectures that, for any prime $p$, if a $p$-block $A$ of a finite group $G$ has an abelian defect group $P$, then $A$ and its…

We introduce a class of complex surface singularities - the blow-$ADE$ singularities - which are likely to be stable with respect to $\mu^*$-constant deformations. We prove such a stability property in several special cases. Here, we…

This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.

We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we prove the stability theorems for odd unitary $K_1$-functor without using the corresponding result from linear $K$-theory under the…

We find stability conditions ([Do], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent…