ﻻ يوجد ملخص باللغة العربية
We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity C^r, r at least 1. In particular, in dimension 3, this gives a very simple proof of Thurstons 1976 regularization theorem without using Mathers homology equivalence.
We prove that if a contact manifold $(M,xi)$ is supported by a planar open book, then Euler characteristic and signature of any Stein filling of $(M,xi)$ is bounded. We also prove a similar finiteness result for contact manifolds supported by spinal
We give an elementary topological obstruction for a $(2q{+}1)$-manifold $M$ to admit a contact open book with flexible Weinstein pages: if the torsion subgroup of the $q$-th integral homology group is non-zero, then no such contact open book exists.
We present new open manifolds that are not homeomorphic to leaves of any C^0 codimension one foliation of a compact manifold. Among them are simply connected manifolds of dimension 5 or greater that are non-periodic in homotopy or homology, namely in their 2-dimensional homotopy or homology groups.
Every open manifold L of dimension greater than one has complete Riemannian metrics g with bounded geometry such that (L,g) is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometr
A book $B_n$ is a graph which consists of $n$ triangles sharing a common edge. In this paper, we study Ramsey numbers of quadrilateral versus books. Previous results give the exact value of $r(C_4,B_n)$ for $1le nle 14$. We aim to show the exact valu