ترغب بنشر مسار تعليمي؟ اضغط هنا

Manifolds that are not leaves of codimension one foliations

198   0   0.0 ( 0 )
 نشر من قبل Paul Schweitzer SJ
 تاريخ النشر 2011
  مجال البحث
والبحث باللغة English
 تأليف Fabio S. Souza




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

229 - Paul A. Schweitzer 2009
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.
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 show that the classical example $X$ of a 3-dimensional generalized manifold constructed by van Kampen is another example of not homologically locally connected (i.e. not HLC) space. This space $X$ is not locally homeomorphic to any of the compact metrizable 3-dimensional manifolds constructed in our earlier paper which are not HLC spaces either.
We define Seiberg-Witten equations on closed manifolds endowed with a Riemannian foliation of codimension 4. When the foliation is taut, we show compactness of the moduli space under some hypothesis satisfied for instance by closed K-contact manifold s. Furthermore, we prove some vanishing and non-vanishing results and we highlight that the invariants may be used to distinguish different foliations on diffeomorphic manifolds.
159 - V. Ferrer , I. Vainsencher 2020
The space of holomorphic foliations of codimension one and degree $dgeq 2$ in $mathbb{P}^n$ ($ngeq 3$) has an irreducible component whose general element can be written as a pullback $F^*mathcal{F}$, where $mathcal{F}$ is a general foliation of degre e $d$ in $mathbb{P}^2$ and $F:mathbb{P}^ndashrightarrow mathbb{P}^2$ is a general rational linear map. We give a polynomial formula for the degrees of such components.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا