Related papers: Open Saturated Sets Without Holonomy

Our aim is to support the choice of two remarkable connections with torsion in a 3-Sasakian manifold, proving that, in contrast to the Levi-Civita connection, the holonomy group in the homogeneous cases reduces to a proper subgroup of the…

In this Note we establish a relation between sections in globally generated holomorphic vector bundles on K\"ahler manifolds, isotropic with respect to a non-degenerate quadratic form, and totally geodesic foliations on Euclidean open…

We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincar\'{e} duality complexes in which a loop of a product…

For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a…

We define a sutured cobordism category of surfaces with boundary and 3-manifolds with corners. In this category a sutured 3-manifold is regarded as a morphism from the empty surface to itself. In the process we define a new class of…

Work of Hofer--Wysocki--Zehnder has shown that many spaces of pseudoholomorphic curves that arise when studying symplectic manifolds may be described as the zero set of a polyfold Fredholm section. This framework has many analytic…

We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…

We consider the topology for a class of hypersurfaces with highly nonisolated singularites which arise as exceptional orbit varieties of a special class of prehomogeneous vector spaces, which are representations of linear algebraic groups…

We prove that the set of leaves of a holomorphic lamination of codimension one that are non-transversal to a germ of a holomorphic map is discrete.

We classify nonsingular holomorphic distributions of arbitrary codimension on certain Hopf manifolds. We prove that all holomorphic distribution of codimension k on a generic Hopf manifold is induced by a mononial holomorphic k-form.

We show that the first twisted cohomology group associated to closed 1-forms on compact manifolds is related to certain 2-dimensional representations of the fundamental group. In particular, we construct examples of nowhere-vanishing…

For every $d\ge 3$, we construct a noncompact smooth $d$-dimensional Riemannian manifold with strictly positive sectional curvature without isoperimetric sets for any volume below $1$. We construct a similar example also for the relative…

We prove that any holomorphic codimension 1 foliation on the complex projective plane has at most one singular point up to the action of an ad-hoc birational self map of the complex projective plane into itself. Consequently, any algebraic…

The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…

Computations based on explicit 4-periodic resolutions are given for the cohomology of the finite groups G known to act freely on S^3, as well as the cohomology rings of the associated 3-manifolds (spherical space forms) M = S^3/G. Chain…

In this paper we study the structure of polynomials of degree three and four that have high bias or high Gowers norm, over arbitrary prime fields. In particular we obtain the following results. 1. We give a canonical representation for…

It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its…

Without the axiom of choice, the free exact completion of the category of sets (i.e. the category of setoids) may not be complete or cocomplete. We will show that nevertheless, it can be enhanced to a derivator: the formal structure of…

Let $D\subset \C^n,$ $G\subset \C^m$ be open sets, let $A$ (resp. $B$) be a subset of the boundary $\partial D$ (resp. $\partial G$) and let $W$ be the 2-fold boundary cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ An open subset…

Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes…