Related papers: Three homological invariants under cleft extension…
In this article, we present the first half of our project on the Iwasawa theory of higher rank Galois deformations over deformations rings of arbitrary dimension. We develop a theory of Coleman maps for a very general class of coefficient…
We define relative versions of the classical invariants of Legendrian and transverse knots in contact 3-manifolds for knots that are homologous to a fixed reference knot. We show these invariants are well-defined and give some basic…
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…
In this article we prove that, under certain hypotheses, Morita context algebras that have zero bimodule morphisms have finite $\phi$-dimension. We also study the behaviour of the $\phi$-dimension for an algebra and its opposite. In…
In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The…
We construct a (non K\"ahler) compact complex 3-dimensional manifold $X$ having two following properties: 1) for any domain $D$ in $C^2$ every meromorphic map $f$ from this domain into $X$ extends to a meromorphic map from the envelope of…
Given a factor map $p : (X,T) \to (Y,S)$ of Cantor minimal systems, we study the relations between the dimension groups of the two systems. First, we interpret the torsion subgroup of the quotient of the dimension groups $K_0(X)/K_0(Y)$ in…
This study focuses on the analysis of derivations, centroids, and inner derivations of 5-dimensional complex nilpotent associative algebras. It presents the classification of these algebras of dimension less than five, as well as the…
In the framework of algebraic quantum field theory, we study the category \Delta_BF^A of stringlike localised representations of a net of observables O \mapsto A(O) in three dimensions. It is shown that compactly localised (DHR)…
Asaeda-Przytycki-Sikora, Manturov, and Gabrov\v{s}ek extended Khovanov homology to links in $\mathbb{RP}^3$. We construct a Lee-type deformation of their theory, and use it to define an analogue of Rasmussen's s-invariant in this setting.…
We show that the difference of the extension dimensions of two derived equivalent algebras is bounded above by the minimal length of a tilting complex associated with a derived equivalence, and that the extension dimension is an invariant…
Let $\mathscr{A}$ be a small abelian category. For a closed subbifunctor $F$ of $\Ext_{\mathscr{A}}^{1}(-,-)$, Buan has generalized the construction of the Verdier's quotient category to get a relative derived category, where he localized…
We introduce and study bi-Lipschitz-invariant dimensions that range between the box and Assouad dimensions. The quasi-Assouad dimensions and $\theta$-spectrum are other special examples of these intermediate dimensions. These dimensions are…
In this paper, we investigate properties of the bounded derived category of finite dimensional modules over a gentle or skew-gentle algebra. We show that the Rouquier dimension of the derived category of such an algebra is at most one.…
Definable subcategories may be extended along a ring homomorphism directly, by using their defining conditions in the new module category, or by tensoring up with the new ring. We investigate what is preserved and reflected by these…
Study of the quotient module of a finite-dimensional Hopf subalgebra pair in order to compute its depth yields a relative Maschke Theorem, in which semisimple extension is characterized as being separable, and is therefore an ordinary…
This short survey, which was written to accompany a minicourse at the BIRS conference "Topology in dimension 4.5", concerns invariants of knotted $2$-spheres in $S^4$, also known as $2$-knots. It covers invariants extracted from the…
For each relative $\operatorname{GL}(V)$-invariant tensor $I\in \Lambda^{p_1+1}V^{\vee}\otimes .. \otimes \Lambda^{p_n+1}V^{\vee}$ we construct a $\operatorname{GL}(V)$-invariant weighted differential form $\eta$ on $(\mathbb{P} V)^{n}$.…
We introduce and develop an analogous of the Auslander-Buchweitz approximation theory (see \cite{AB}) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results…
We construct a new family of Type IIB backgrounds that are dual to five dimensional conformal field theories compactified and deformed by VEVs of certain operators. This generates an RG flow into a smooth background dual to non-SUSY gapped…