محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Preprint |
| منشور في: |
2015
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://arxiv.org/abs/1502.04470 |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
جدول المحتويات:
- For a smooth manifold $N$ denote by $E^m(N)$ the set of smooth isotopy classes of smooth embeddings $N\to\mathbb R^m$. A description of the set $E^m(S^p\times S^q)$ was known only for $p=q=0$ or for $p=0$, $m\ne q+2$ or for $2m\ge 2(p+q)+\max\{p,q\}+4$. (The description was given in terms of homotopy groups of spheres and of Stiefel manifolds.) For $m\ge2p+q+3$ we introduce an abelian group structure on $E^m(S^p\times S^q)$ and describe this group `up to an extension problem'. This result has corollaries which, under stronger dimension restrictions, more explicitly describe $E^m(S^p\times S^q)$. The proof is based on relations between sets $E^m(N)$ for different $N$ and $m$, in particular, on a recent exact sequence of M. Skopenkov.