arXiv research

Simply-connected shrinking Kähler-Ricci solitons are proven.

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…

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…

Simply connected spaces of tight frames identified.

Minimal graphs over simply connected domains grow at most exponentially.

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…

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…

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.

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

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

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.

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

To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence questio…

The paper proves conditions for Kähler and Riemannian manifolds to be simply connected.

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

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…

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),…

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

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.

3D Schoenflies theorem for simply-connected 2-complexes.

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…

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…

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.

One proves that there exists an obstruction to an open simply connected $n$-manifold of dimension $n\geq 5$ being geometrically simply connected. In particular there exist uncountably many simply connected $n$-manifolds which are not w.g.s.c. One proves that for $n\neq 4$ an $n$-manifold proper homotopy equivalent to a…

We derive Verlinde's formula from the fixed point formula for loop groups proved in the companion paper "A fixed point formula for loop group actions", and extend it to compact, connected groups that are not necessarily simply-connected.

Study on negative Sasakian structures on specific 5-manifolds.

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

Study compact PL 4-manifolds with special handle decompositions.

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.

We characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lovász, Pardon and Wagner.

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.