Related papers: Four dimensional almost complex torus manifolds

We extend the tropical intersection theory to tropicalizations of germs of analytic sets. In particular, we construct a (not entirely obvious) local version of the ring of tropical fans with a nondegenerate intersection pairing. As an…

We give several explicit examples of compact manifolds with a $1$-parameter family of almost complex structures having arbitrarily small Nijenhuis tensor in the $C^0$-norm. The $4$-dimensional examples possess no complex structure, whereas…

By works of Schoen-Yau and Gromov-Lawson any Riemannian manifold with nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov conjectured subconvergence of tori with respect to a weak Sobolev type…

Let $X$ be a compact complex Calabi-Yau 4-fold. Under certain assumptions, we define Donaldson-Thomas type deformation invariants ($DT_{4}$ invariants) by studying moduli spaces of solutions to the Donaldson-Thomas equations on $X$. We also…

In this work we consider a class of contact manifolds $(M,\eta)$ with an associated almost contact metric structure $(\phi, \xi, \eta,g)$. This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class…

Let $M$ be any compact four-dimensional PL-manifold with or without boundary (e.g. the four-dimensional sphere or ball). Consider the space $T(M)$ of all simplicial isomorphism classes of triangulations of $M$ endowed with the metric…

In the space of couplings of the 4D N=1 gauge theory associated to D3 branes probing Calabi-Yau singularities, there is a manifold over which superconformal invariance is preserved. The AdS/CFT correspondence is valid precisely for this…

Let $M$ be a complete Riemannian manifold and suppose $p\in M$. For each unit vector $v \in T_p M$, the $\textit{Jacobi operator}$, $\mathcal{J}_v: v^\perp \rightarrow v^\perp$ is the symmetric endomorphism, $\mathcal{J}_v(w) = R(w,v)v$.…

In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of…

We provide a algebro-geometric combinatorial description of geometrically integral geometrically normal varieties endowed with an effective action of an algebraic torus over arbitrary fields. This description is achieved in terms of…

Locally standard $T$-pseudomanifolds were introduced by the authors in a previous work. They are topological stratified pseudomanifolds equipped with torus actions. Their equivariant homeomorphism types are classified by characteristic data…

We present complete simplicial fan realizations of any spherical subword complex of type $A_n$ for $n\leq 3$. This provides complete simplicial fan realizations of simplicial multi-associahedra $\Delta_{2k+4,k}$, whose facets are in…

Let (M,\omega) be a four dimensional compact connected symplectic manifold. We prove that (M,\omega) admits only finitely many inequivalent Hamiltonian effective 2-torus actions. Consequently, if M is simply connected, the number of…

The main objects of this paper are torus orbifolds that have exactly two fixed points. We study the equivariant topological type of these orbifolds and consider when we can use the results of the paper [DKS] (arXiv:1809.03678) to compute…

I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…

A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A…

Let $\Delta$ be a $d$-dimensional normal pseudomanifold, $d \ge 3.$ A relative lower bound for the number of edges in $\Delta$ is that $g_2$ of $\Delta$ is at least $g_2$ of the link of any vertex. When this inequality is sharp $\Delta$ has…

A classification theorem for 4-dimensional conformally flat QK3-manifolds is proved.

A 4-dimensional Riemannian manifold equipped with a circulant structure, which is an isometry with respect to the metric and its fourth power is the identity, is considered. The almost product manifold associated with the considered…

Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…