Related papers: Small Seifert 3-manifolds with non-reduced $\mathr…

We study modular invariance of normalized supercharacters of tame integrable modules over an affine Lie superalgebra, associated to an arbitrary basic Lie superalgebra $ \mathfrak{g}. $ For this we develop a several step modification…

Let $G$ be a finite group. Denote by $\textrm{Irr}(G)$ the set of all irreducible complex characters of $G.$ Let $\textrm{cd}(G)=\{\chi(1)\;|\;\chi\in \textrm{Irr}(G)\}$ be the set of all irreducible complex character degrees of $G$…

Let $X$ be a Stein manifold of dimension at least 3. Given a compact codimension 2 real analytic submanifold $M$ of $X$, that is the boundary of a compact Levi-flat hypersurface $H$, we study the regularity of $H$. Suppose that the CR…

We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of…

A 7-dimensional area-minimizing embedded hypersurface $M$ will in general have a discrete singular set. The same is true if $M$ is stable, or has bounded index, provided $H^6(sing M) = 0$. We show that if $M_i$ are a sequence of such…

Let M be a closed orientable Seifert fibered 3-manifold with a hyperbolic base 2-orbifold, or equivalently, admitting a geometry modeled on H^2 \times R or the universal cover of SL(2,R). Our main result is that the connected component of…

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order…

Let $\mathbf{K}$ be the class of countable structures $M$ with the strong small index property and locally finite algebraicity, and $\mathbf{K}_*$ the class of $M \in \mathbf{K}$ such that $acl_M(\{ a \}) = \{ a \}$ for every $a \in M$. For…

Symplectic 4-manifolds $(X,\omega)$ with $b_+{=}1$ are roughly classified by the canonical class $K$ and the symplectic form $\omega$ depending upon the sign of $K^2$ and $K\cdot \omega$. Examples are known for each category except for the…

A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial…

The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is…

The closed subalgebra $\mathcal J$ of the Banach algebra $\mathcal L(X)$ of bounded linear operators on the Banach space $X$ is a non-trivial closed $\mathcal I$-subideal of $\mathcal L(X)$ if $\mathcal I$ is a closed ideal of $\mathcal…

We prove a global local rigidity result for character varieties of 3-manifolds into $\rm{SL}_2$. Given a 3-manifold with toric boundary $M$ satisfying some technical hypotheses, we prove that all but a finite number of its Dehn fillings…

We find conditions which ensure that the topological complexity of a closed manifold $M$ with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on…

We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$.…

In this paper we consider closed $\text{SL}(3,\mathbb{C})$-structures which are either mean convex or tamed by a symplectic form. These notions were introduced by Donaldson in relation to $\text{G}_2$-manifolds with boundary. In particular,…

We study the automorphism group of a compact 7-manifold $M$ endowed with a closed non-parallel G$_2$-structure, showing that its identity component is abelian with dimension bounded by min$\{6,b_2(M)\}$. This implies the non-existence of…

In this paper, we give an improved Morse index bound of minimal hypersurfaces from Almgren-Pitts min-max construction in any closed Riemannian manifold $M^{n+1}$ $(n+1 \geq 3$), which generalizes a result by X. Zhou…

In this note, we determine the irreducible characters for the simple algebraic groups of type $A_5$ over an algebraically closed field $K$ of characteristic 3, by using a theorem of Xi Nanhua and the Matlab software. In order to obtain…

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $su(n,n)$. Earlier were given the main multiplets of indecomposable elementary…