In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L-cohomology of these manifolds: if e.g. a manifold admits a metric of bounded geometry which outside a compact set has nonnegative Ricci curvature and nonnegative mean curvature (of the bo...

In this paper, an explicit classification result for certain 5-manifolds with fundamental group Z/2 is obtained. These manifolds include total spaces of circle bundles over simply-connected 4-manifolds.

‎in this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎we show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a lie groupoid‎. ‎using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the lie algebra of all vector fields on the smooth...

Recently, the notion of data as manifolds has come into being. The subject of image manifolds has been explored but not extensively and not from the point of view of di erential geometry. It is a well known fact that image manifolds are curved. Using some basic techniques of di erential geometry this paper explores image manifold curvature and attempts get a feel for the magnitude of this curva...

In these notes we discuss obstructions to the existence of local invariant manifolds in some smoothness class, near hyperbolic fixed points of diffeomorphisms. We present an elementary construction for continuously differentiable invariant manifolds, that are not necessarily normally hyperbolic, near attracting fixed points. The analogous theory for invariant manifolds near hyperbolic equilbria...

This paper contains an approach to compute Taylor approximations of invariant manifolds associated with arbitrary fixed reference solutions of nonautonomous difference equations. Our framework is sufficiently general to include, e.g., stable and unstable manifolds of periodic orbits, or classical center-stable/-unstable manifolds corresponding to equilibria. In addition, our focus is to give ap...

In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds . We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities. Connected components of the complement of this hypersurface correspond to homeomorphism type of spin 3-manifolds. This suggests the natural axiomatics of Vassiliev...

The construction of new hyperkähler manifolds by taking the infinite monopole mass limit of certain BPS monopole moduli spaces is considered. The one-parameter family of hyperkähler manifolds due to Dancer is shown to be an example of such manifolds. A new family of fixed monopole spaces is constructed. They are the moduli spaces of four SU4 monopoles, in the infinite mass limit of two of the m...

Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known tight triangulated manifolds are stacked. It is known that locally stacked tight triangulated manifolds are strongly minimal. Except for three infinite series ...

A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold M̃ with the deck transform group acting conformally on M̃ . If M admits a holomorphic flow, acting on M̃ conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vaisman manifolds is stable under small deformations. We define a new class of LCK-manifolds, called LCK manifo...