Related papers: Amalgams, connectifications, and homogeneous compa…
We describe a class of compact $G_2$ orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective…
In this paper we give conditions under which a topological semigroup can be embedded algebraically and topologically into a compact topological group. We prove that every feebly compact regular first countable cancellative commutative…
We study the homotopy type of the harmonic compactification of the moduli space of a 2-cobordism S with one outgoing boundary component, or equivalently of the space of Sullivan diagrams of type S on one circle. Our results are of two…
Let $\Delta$ be a spherical building each of whose irreducible components is infinite, has rank at least 2 and satisfies the Moufang condition. We show that $\Delta$ can be given the structure of a topological building that is compact and…
It is well known that a compact two dimensional surface is homeomorphic to a polygon with the edges identified in pairs. This paper not only presents a new proof of this statement but also generalizes it for any connected n-dimensional…
We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\operatorname{sec}|\leq 1$. Moreover, we show that the set of geometric models is compact in the…
We discuss gauge-fixing, propagators and effective potentials for topological A-brane composites in Calabi-Yau compactifications. This allows for the construction of a holomorphic potential describing the low-energy dynamics of such…
The following paper is inspired by Efimov's problem - an undecided problem of whether there exists an infinite compact topological space that does not contain neither non-trivial convergent sequences nor a copy of $\beta\omega$. After…
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine…
It is shown that a connected non-compact metrizable manifold of dimension $\ge 2$ is strongly discrete homogeneous if and only if it has one end (in the sense of Freudenthal compactification).
We classify the connected-homogeneous digraphs with more than one end. We further show that if their underlying undirected graph is not connected-homogeneous, they are highly-arc-transitive.
On compact K\"ahler manifolds, we relate ABC Massey products arising from complex analytic cycles to holomorphic linking numbers. This enables us to construct a family of simply connected projective 3-folds with trivial canonical bundle,…
We construct holomorphic maps with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained in the domain of definition of the map. Our examples are injective and defined on a…
We compare two combinatorial models for the moduli space of two-dimensional cobordisms: B\"odigheimer's radial slit configurations and Godin's admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map.…
We show that for a closed surface of genus at least 5, or a surface of genus at least 2 with at least one marked point, the set of uniquely ergodic foliations and the set of cobounded foliations is path-connected and locally path-connected.
We prove that the space $\mathcal{H}_\infty$ of framed infinite volume hyperbolic $3$-manifolds is connected but not path connected. Two proofs of connectivity of this space, which is equipped with the geometric topology, are given, each…
We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many…
The goal of this paper is the construction of a compact manifold with G$_2$ holonomy and nodal singularities along circles using twisted connected sum method. This paper finds matching building blocks by solving the Calabi conjecture on…
If $\mathcal P$ is a family of filters over some set $I$, a topological space $X$ is \emph{sequencewise $\mathcal P$-\brfrt compact} if, for every $I$-indexed sequence of elements of $X$, there is $F \in \mathcal P$ such that the sequence…
Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter.