ترغب بنشر مسار تعليمي؟ اضغط هنا

Embedded spheres and 4-manifolds with spin coverings

288   0   0.0 ( 0 )
 نشر من قبل Christian Bohr
 تاريخ النشر 2001
  مجال البحث
والبحث باللغة English
 تأليف Christian Bohr




اسأل ChatGPT حول البحث

A strategy for constructing an embedded sphere in a 4-manifold realizing a given homology class which has been successfully applied in the past is to represent the class as a first step stably by an embedded sphere, i.e. after adding products of 2-spheres, and to move that sphere back into the original manifold. In this paper, we study under what conditions the first step of this approach can be carried out if the 4-manifold at hand is not simply connected. One of our main results is that there are - apart from the well known Arf invariant - additional bordism theoretical obstructions to stably representing homology classes by embedded spheres.



قيم البحث

اقرأ أيضاً

94 - Christian Bohr 2000
It is one of the most important facts in 4-dimensional topology that not every spherical homology class of a 4-manifold can be represented by an embedded sphere. In 1978, M. Freedman and R. Kirby showed that in the simply connected case, many of the obstructions to constructing such a sphere vanish if one modifies the ambient 4-manifold by adding products of 2-spheres, a process which is usually called stabilisation. In this paper, we extend this result to non-simply connected 4-manifolds and show how it is related to the Spin^c-bordism groups of Eilenberg-MacLane spaces.
We prove that for 4-manifolds $M$ with residually finite fundamental group and non-spin universal covering $Wi M$, the inequality $dim_{mc}Wi Mle 3$ implies the inequality $dim_{mc}Wi Mle 2$.
107 - Christopher Scaduto 2018
We show that the set of even positive definite lattices that arise from smooth, simply-connected 4-manifolds bounded by a fixed homology 3-sphere can depend on more than the ranks of the lattices. We provide two homology 3-spheres with distinct sets of such lattices, each containing a distinct nonempty subset of the rank 24 Niemeier lattices.
In this paper we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a 1-orbifold.
73 - Igor Nikolaev 2019
We construct a functor from the smooth 4-dimensional manifolds to the hyper-algebraic number fields, i.e. fields with non-commutative multiplication. It is proved that that the simply connected 4-manifolds correspond to the abelian extensions. We rec over the Rokhlin and Donaldsons Theorems from the Galois theory of the non-commutative fields.
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