اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHaefligers codimension-one singular foliations, open books and twisted open books in dimension 3
361
0
0.0
(
0
)
تأليف
Francois Laudenbach
اسأل ChatGPT حول البحث
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.
قيم البحث
اقرأ أيضاً
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
open books with planar pages. Moving beyond the geography of Stein fillings, we classify fillings of some lens spaces.
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 achieve this by proving that a symplectomorphism of a flexible Weinstein manifold acts trivially on cohomology. We also produce examples of non-trivial loops of flexible contact structures using related ideas.
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
y of (L,g) suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the `bounded homology property, a semi-local property of (L,g) that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential step involves a partial generalization of the Novikov closed leaf theorem to higher dimensions.
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
e of $r(C_4,B_n)$ for infinitely many $n$. To achieve this, we first prove that $r(C_4,B_{(m-1)^2+(t-2)})le m^2+t$ for $mge4$ and $0 leq t leq m-1$. This improves upon a result by Faudree, Rousseau and Sheehan (1978) which states that begin{align*} r(C_4,B_n)le g(g(n)), ;;text{where};;g(n)=n+lfloorsqrt{n-1}rfloor+2. end{align*} Combining the new upper bound and constructions of $C_4$-free graphs, we are able to determine the exact value of $r(C_4,B_n)$ for infinitely many $n$. As a special case, we show $r(C_4,B_{q^2-q-2}) = q^2+q-1$ for all prime power $qge4$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
