arXiv research

Simply-connected shrinking Kähler-Ricci solitons are proven.

Research shows RCD* spaces are semi-locally simply connected.

The paper characterizes simply connected quandles using cocycles with prime values.

We prove that an open 3-manifold proper homotopy equivalent to a geometrically simply connected polyhedron is simply connected at infinity, generalizing a theorem of V.Poenaru.

We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, ``can one hear the shape of a drum?'' In order to construct simply connected examples, we exploit the observation that an orbifold whose unde…

Minimal graphs over simply connected domains grow at most exponentially.

We compute all the simply connected homogeneous and infinitesimally homogeneous surfaces admitting one or more invariant affine connections. We find exactly six non equivalent simply connected homogeneous surfaces admitting more than one invariant connections and four classes of simply connected homogeneous surfaces ad…

Defines spectral varieties for non-simply connected manifolds and constructs conformal invariants.

We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic…

Classifies 3D spaces using specific invariants.

Ricci limit spaces are semi-locally simply connected.

Simply-connected 4-manifolds are covered by products with a 2-torus.

We completely determine which simply connected rational homology 5-spheres admit Sasaki-Einstein metrics.

Circle's metric is at least π/4 away from any simply connected geodesic space.

This paper computes the obstruction to the existence of equivariant extensions of basic gerbes over non-simply connected compact simple Lie groups. By modifying a (finite dimensional) construction of Gawȩdzki-Reis [J. Geom. Phys. 50(1):28-55, 2004], we exhibit basic equivariant bundle gerbes over non-simply connected c…

The study refines known counterexamples in 4D to satisfy certain inequalities.

Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts by a noncontractible n-dimensional Peano cont…

We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.

Simply connected spaces of tight frames identified.

We show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian $(n+2)$-manifold, with regular leaves homeomorphic to the $n$-torus, is given by a smooth effective $n$-torus action. This solves in the negative for the codimension $2$ case a question about the existence of foliat…

Several authors have recently attempted to show that the intersection of three simply connected subcontinua of the plane is simply connected provided it is non-empty and the intersection of each two of the continua is path connected. In this note we give a very short complete proof of this fact. We also confirm a relat…

We compute the equivariant $K$-theory $K_G^*(G)$ for a simply connected Lie group $G$ (acting on itself by conjugation). We prove that $K_G^*(G)$ is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also study a special example of a non-simply connected Lie group $G$, namely PSU(3),…

Study on spheres in simply-connected 4-manifolds with abelian complements.

We construct a compact simply-connected 7-dimensional manifold admitting a K-contact structure but not a Sasakian structure. We also study rational homotopy properties of such manifolds, proving in particular that a simply-connected 7-dimensional Sasakian manifold has vanishing cup-product on the second cohomology and …

In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group $\Z$. In this paper, we also produce the first examples of simply con…

We produce infinite families of exotic actions of finite cyclic groups on simply connected smooth 4-manifolds with nontrivial Seiberg-Witten invariants.

We construct a group (an HNN extension of a free group) with polynomial isoperimetric function, linear isodiametric function and non-simply connected asymptotic cones.

Monodromy and vanishing cycles computed for ample linear systems on simply connected surfaces.

We will describe some results regarding the algorithmic nature of homeomorphism problems for manifolds; in particular, the following theorem. Theorem 1: Every PL or smooth simply connected manifold M^n of dimension n at least 5 can be recognized among simply connected manifolds. That is, there is an algorithm to decide…

New invariant P helps classify simply-connected 8-manifolds.

Study determines homotopy types of specific 6-manifolds.

The boundary of hyperbolic groups is locally simply connected.

Study knotted surfaces in simply-connected 4-manifolds with trivial boundary.

This paper shows the reduced characteristic group of Lie LCP manifolds is simply connected.

Proves Rudyak's conjecture for low-dimensional simply connected spin manifolds.

Simply connected moduli space of Ricci flat metrics on K3 surfaces.

For each pair $(e,σ)$ of integers satisfying $2e+3σ\ge 0$, $σ\leq -2$, and $e+σ\equiv 0\pmod{4}$, with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic $e$ and signature $σ$. We also produce simply connected, minimal symplectic 4-manifolds with signature zero (re…

We determine the cut locus of arbitrary non-simply connected, compact and irreducible Riemannian symmetric space explicitly, and compute injectivity radius and diameter for every type of them.

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.

We prove that simply connected open Riemannian manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.

We show that the Cheeger isoperimetric constant of a solvable simply connected Lie group $G$ with Lie algebra $\G$ is $h(G)=\max_{H\in\G,||H||=1} \tr(\ad (H))$.

Minimal hyperbolic foliations on 3-manifolds have non-simply connected generic leaves.

Simply-connected surfaces of general type for n≥5.

Shells resist three out of six possible loads if simply connected.

Study cohomotopy sets of simply connected 7-manifolds using suspension decompositions.

Simply connected 4-manifolds with specific Weyl tensor are geodesic balls in space forms.

We attach copies of the circle to points of a countable dense subset $D$ of a separable metric space $X$ and construct an earring space $E(X,D)$. We show that the fundamental group of $E(X,D)$ is isomorphic to a subgroup of the Hawaiian earring group, if the space $X$ is simply-connected and locally simply-connected. I…

For each rational homology 3-sphere $Y$ which bounds simply connected definite 4-manifolds of both signs, we construct an infinite family of irreducible rational homology 3-spheres which are homology cobordant to $Y$ but cannot bound any simply connected definite 4-manifold. As a corollary, for any coprime integers $p,…