Related papers: Dual 2-complexes in 4-manifolds

We study random 2-dimensional complexes in the Linial - Meshulam model and prove that for the probability parameter satisfying $$p\ll n^{-46/47}$$ a random 2-complex $Y$ contains several pairwise disjoint tetrahedra such that the 2-complex…

We give a new perspective of Heegaard splittings in terms square complexes and Guirardel's notion of a \textit{core} which allows for combinatorial measurement of the obstruction to being a connect sum of Heegaard diagrams. A Heegaard…

Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a…

We study the twisted Hochschild homology of quantum full flag manifolds, with the twist being the modular automorphism of the Haar state. We show that non-trivial 2-cycles can be constructed from appropriate invariant projections. The main…

In this note we study whether specific elements in the second homology of specific simply connected closed $4$-manifolds can be represented by smooth or topologically flat embedded spheres.

In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-K\"ahler manifold is a…

A regular bipartite tournament is an orientation of a complete balanced bipartite graph $K_{2n,2n}$ where every vertex has its in- and outdegree both equal to $n$. In 1981, Jackson conjectured that any regular bipartite tournament can be…

We show that, in addition to SO(4), the Hubbard model at half filling on a bipartite lattice has a group of discrete symmetries and transformations. A unique Hubbard-Stratonovich decomposition of the interaction term, incorporating both…

Here we study the deformations of associative submanifolds inside a G_2 manifold M^7 with a calibration 3-form \phi. A choice of 2-plane field \Lambda on M (which always exits) splits the tangent bundle of M as a direct sum of a…

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper…

We study the algebraic properties of the five-parameter family $H(t_1,t_2,t_3,t_4;q)$ of double affine Hecke algebras of type $C^\vee C_1$. This family generalizes Cherednik's double affine Hecke algebras of rank 1. It was introduced by…

We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By…

For a smoothing Y of a 2-dimensional cyclic quotient singularity X, we construct a simple handle decomposition of Y by using a particular birational map from Y to the projective plane. The manifold Y is built up from the product of an…

Let $k$, $\lambda$ and $\mu$ be positive integers. A decomposition of a multigraph $ \lambda G$ into edge-disjoint subgraphs $G_1, \ldots , G_k$ is said to be \emph{enclosed} by a decomposition of a multigraph $\mu H$ into edge-disjoint…

We study deformations of the Howe dual pairs $(\mathrm{U}(n),\mathfrak{u}(1,1))$ and $(\mathrm{U}(n),\mathfrak{u}(2|1))$ to the context of a rational Cherednik algebra $H_{1,c}(G,E)$ associated with a real reflection group $G$ acting on a…

We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loeh up to dimension five. More…

By studying the Higgs bundle equations with the gauge group replaced by the group of symplectic diffeomorphisms of the 2-sphere we encounter the notion of a folded hyperkaehler 4-manifold and conjecture the existence of a family of such…

Let $M$ be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $\chi(M)\ne 0$. We show that if $G$ is a finite group of 2-rank $\le 1$ which admits a homologically…

We show that any 4-manifold admitting a $(g;k_1,k_2,0)$-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in $S^4$, smoothly embedded except for one singular point which is the cone on a link. A…

We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes…