Related papers: The round handle problem
Every closed oriented PL 4-manifold is a branched cover of the 4-sphere branched over a PL-surface with finitely many singularities by Piergallini [Topology 34(3):497-508, 1995]. This generalizes a long standing result by Hilden and…
In one of their seminal articles on allowable sequences, Goodman and Pollack gave combinatorial generalizations for three problems in discrete geometry, one of which being the Dirac conjecture. According to this conjecture, any set of $n$…
We answer in negative two of questions posed in [4]. We also establish a new characterization of semiprime left Goldie rings by showing that a semiprime ring R is left Goldie iff it is regular left fusible and has finite left Goldie…
In-hand manipulation is a crucial ability for reorienting and repositioning objects within grasps. The main challenges in this are not only the complexity of the computational models, but also the risks of grasp instability caused by active…
For 3-manifolds with torus boundary, the bordered Heegaard Floer invariants of Lipshitz--Ozsv\'ath--Thurston have a geometric interpretation as immersed multi-curves with local systems in the punctured torus according to the work of…
The lift of K-theoretic D-brane charge to M-theory was recently hypothesized to land in Cohomotopy cohomology theory. To further check this "Hypothesis H", here we explicitly compute the constraints on fractional D-brane charges at…
We give a method for obtaining a handle decomposition of an $n$-manifold if the manifold is given by isometric side-pairings of a polyhedron in $\en$, $\sn$ or $\hn$. Every cycle of $k$-faces on the polyhedron corresponds to an…
In this article, we study a class of closed connected orientable PL $4$-manifolds admitting a semi-simple crystallization and which have an infinite cyclic fundamental group. We show that the manifold in the class admits a handle…
It is known that for coprime integers $p>q\geq 1$, the lens space $L(p^2,pq-1)$ bounds a rational ball, $B_{p,q}$, arising as the 2-fold branched cover of a (smooth) slice disk in $B^4$ bounding the associated 2-bridge knot. Lekilli and…
An oriented link L in a 3-sphere S in complex 2-space is a C-boundary if it bounds a piece of algebraic curve in the 4-ball bounded by S. Using Kronheimer and Mrowka's proof of the Thom Conjecture, we construct many oriented knots which are…
We propose a theory to explain the formation of spiral arms and of all types of outer rings in barred galaxies, extending and applying the technique used in celestial mechanics to compute transfer orbits. Thus, our theory is based on the…
We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of…
This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions.…
Given a link L in the 3-sphere, we ask whether the components of L bound disjoint, nullhomologous disks properly embedded in a simply-connected positive-definite smooth 4-manifold; the knot case has been studied extensively in work of…
We apply Donaldson's theorem on the intersection forms of definite 4--manifolds to characterize the lens spaces which smoothly bound rational homology 4--dimensional balls. Our result implies, in particular, that every smoothly slice…
We can construct a 4-manifold by attaching 2-handles to a 4-ball with framing r along the components of a link in the boundary of the 4-ball. We define a link as r-shake slice if there exists embedded spheres that represent the generators…
In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently…
We define branched bending deformations as deformations supported on a piecewise totally geodesic complex of $(n-1)$-dimensional faces meeting along $(n-2)$-dimensional branching loci. These are a generalization of bending deformations, as…
L\'{a}szl\'{o} Fuchs posed the following question: which abelian groups arise as the group of units in a ring? In this paper, we investigate a related question: for such realizable groups $G$, when is there a ring $R$ with unit group $G$…
Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.