On local first order structural stability of pairings of vector fields and functions
On local flatness of manifolds with AHS-structures
Summary: The AHS-structures on manifolds are the simplest cases of the so called parabolic geometries which are modeled on homogeneous spaces corresponding to a parabolic subgroup in a semisimple Lie group. It covers the cases where the negative parts of the graded Lie algebras in question are abelian. In the series the authors developed a consistent frame bundle approach to the subject. Here we give explicit descriptions of the obstructions against the flatness of such structures based on the latter...
On locally Lipschitz locally compact transformation groups of manifolds
In this paper we show that a “locally Lipschitz” locally compact transformation group acting continuously and effectively on a connected paracompact locally Euclidean topological manifold is a Lie group. This is a contribution to the proof of the Hilbert-Smith conjecture. It generalizes the classical Bochner-Montgomery-Kuranishi Theorem[1, 9] and also the Repovš-Ščepin Theorem [17] which holds only for Riemannian manifolds.
On locally -incomparable families of infinite-dimensional Cantor manifolds
The notion of locally -incomparable families of compacta was introduced by K. Borsuk [KB]. In this paper we shall construct uncountable locally -incomparable families of different types of finite-dimensional Cantor manifolds.
On low dimensional S-cobordisms.
On Lusternik-Schnirelmann category of SO(10)
Let G be a compact connected Lie group and p: E → ΣA be a principal G-bundle with a characteristic map α: A → G, where A = ΣA₀ for some A₀. Let with F₀ = ∗, F₁ = ΣK₁ and Fₘ ≃ G be a cone-decomposition of G of length m and F’₁ = ΣK’₁ ⊂ F₁ with K’₁ ⊂ K₁ which satisfy up to homotopy for all i. Then cat(E) ≤ m + 1, under suitable conditions, which is used to determine cat(SO(10)). A similar result was obtained by Kono and the first author (2007) to determine cat(Spin(9)), but that result could not...
On malnormal peripheral subgroups of the fundamental group of a -manifold
Let be a non-trivial knot in the -sphere, its exterior, its group, and its peripheral subgroup. We show that is malnormal in , namely that for any with , unless is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in attached to which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups in the fundamental group of a...
On manifold spines and cyclic presentations of groups
This is a survey of results and open problems on compact 3-manifolds which admit spines corresponding to cyclic presentations of groups. We also discuss questions concerning spines of knot manifolds and regular neighborhoods of homotopically PL embedded compacta in 3-manifolds.
On manifolds diffeomorphic on the complement of a point
We prove that four manifolds diffeomorphic on the complement of a point have the same Donaldson invariants.
On manifolds homeomorphic to ...P2#8... .
On Manifolds Representing Homology Classes in Codimension 2.
On manifolds with finitely generated homotopy groups.
On manifolds with nonhomogeneous factors
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.
On Martinet's singular symplectic structures
On maximal fibred submanifolds of a knot exterior.
On McMullen's and other inequalities for the Thurston norm of link complements.
On measures in fibre spaces
On monodromy of complex projective structures.
On monotone unions of closed n-cells
On Murasugi's and Traczyk's Criteria for Periodic Links.