BIMSA >
Moscow-Beijing topology seminar
The band connected sum and the second Kirby move for higher-dimensional links
The band connected sum and the second Kirby move for higher-dimensional links
Organizers
Vassily Manturov
, Shiquan Ren
,
Zhe Yan Wan
Speaker
Arkadiy Skopenkov
Time
Wednesday, August 21, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580
(141592)
Abstract
Let $f:S^q\sqcup S^q\to S^m$ be an (ordered oriented) 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 $\sigma f:S^q\sqcup S^q\to S^m$ as follows.
The first component of $\sigma f$ is the `standardly shifted' first component of $f$.
The second component of $\sigma f$ is the embedded connected sum of the components of $f$.
How does (the isotopy class of) $\sigma f$ 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 $S^6$.
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 $\sigma f:S^q\sqcup S^q\to S^m$ as follows.
The first component of $\sigma f$ is the `standardly shifted' first component of $f$.
The second component of $\sigma f$ is the embedded connected sum of the components of $f$.
How does (the isotopy class of) $\sigma f$ 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 $S^6$.