-д хадгалсан:
| Үндсэн зохиолч: | |
|---|---|
| Формат: | Preprint |
| Хэвлэсэн: |
2024
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| Нөхцлүүд: | |
| Онлайн хандалт: | https://arxiv.org/abs/2406.15367 |
| Шошгууд: |
Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
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Агуулга:
- Let $f:S^q\sqcup S^q\to S^m$ be a link (i.e. an embedding). How does (the isotopy class of) the knot $S^q\to S^m$ obtained by embedded connected sum of the components of $f$ depend on $f$? Define a link $σf:S^q\sqcup S^q\to S^m$ as follows. The first component of $σf$ is the `standardly shifted' first component of $f$. The second component of $σf$ is the embedded connected sum of the components of $f$. How does (the isotopy class of) $σf$ depend on $f$? How does (the isotopy class of) the link $S^q\sqcup S^q\to S^m$ obtained by embedded connected sum of the last two components of a link $g:S^q_1\sqcup S^q_2\sqcup S^q_3\to S^m$ depend on $g$? We give the answers for the `first non-trivial case' $q=4k-1$ and $m=6k$. The first answer was used by S. Avvakumov for classification of linked 3-manifolds in $S^6$.