相关论文: A Small Polyhedral Z-Acyclic 2-Complex in R4

In this paper we introduce the notion of a $d$-dimensional cycle which is a homological generalization of the idea of a graph cycle to higher dimensions. We examine both the combinatorial and homological properties of this structure and use…

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such…

This is the same version that was previously only on my home page. We give a description of geometric realization which makes it evident that it commutes with products. A similar approach is used to treat cyclic sets. Our approach is…

We consider closed simplicial and cubical $n$-complexes in terms of link of their $(n-2)$-faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every $(n-2)$-face is contained in 3 or 4 $n$-faces. Such simplicial…

Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated…

We prove that a 2-convex closed surface $S\subset E^4$ in the four-dimensional Euclidean space $E^4$, which is either $C^2$-smooth or polyhedral, provided that each vertex is incident to at most five edges, admits a mapping of degree one to…

The vanishing of Van Kampen's obstruction is known to be necessary and sufficient for embeddability of a simplicial n-complex into $R^{2n}$ for $n\neq 2$, and it was recently shown to be incomplete for $n=2$. We use algebraic-topological…

In this paper, we give an example of a chiral 4-polytope in projective 3-space. This example naturally yields a finite chiral 4-polytope in Euclidean 4-space, giving a counterexample to Theorem 11.2 of [2].

Let $X$ be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to $n(-E_8)\bigoplus mH$, where $H$ is the hyperbolic form. In this paper, we prove that for $n$ such that $n\equiv 2 ~{\rm mod} ~4$, there…

In this paper, we investigate the existence of an elementary abelian closure in characteristic not $2$ for biquadratic extensions. We discover that it exists for any non-cyclic extension. We make use of it to obtain a classification for…

Given an irreducible contractible open 3-manifold W which is not homeomorphic to R^3, there is an associated simplicial complex S(W), the complex of end reductions of W. Whenever W covers a 3-manifold M one has that the fundamental group of…

While sporadic examples of virtual resolutions with homology have been constructed, their occurrence is not well understood or controlled. Our results build a new set of tools for studying virtual resolutions of monomial ideals as arising…

We introduce a new model for random simplicial complexes which with high probability generates a complex that has a simply-connected double cover. Hence we develop a model for random simplicial complexes with fundamental group…

We show that for $d\geq 2$ every finite $d$-dimensional simplicial complex is a deformation retract of a $(2d-1)$-dimensional pseudomanifold with boundary. Moreover, it embeds as a retract in a closed $(2d-1)$-dimensional pseudomanifold.

We describe novel local singularity models for $\mathbb Z/2$ harmonic 1-forms, self-dual 2-forms and spinors in dimension 4. These models are homogeneous versions on $\mathbb{R}^4$ whose singular sets are cones on the 1-skeletal of certain…

We present a classification of the so-called "additive symmetric 2-cocycles" of arbitrary degree and dimension over Z/p, along with a partial result and some conjectures for m-cocycles over Z/p, m > 2. This expands greatly on a result…

We investigate the integrability of natural almost complex structures on the twistor space of an almost para-quaternionic manifold as well as the integrability of natural almost paracomplex structures on the reflector space of an almost…

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact $4$-dimensional solvmanifolds without any integrable almost complex structure. According to the classification…

We classify compact complex surfaces which contain a Zariski open subset whose universal covering is the cylinder DxC.

We classify compact surfaces with torsion-free affine connections for which every geodesic is a simple closed curve. In the process, we obtain completely new proofs of all the major results concerning the Riemannian case. In contrast to…