In
geometric topology, a band sum of two ''n''-dimensional
knots
A knot is a fastening in rope or interwoven lines.
Knot may also refer to:
Places
* Knot, Nancowry, a village in India
Archaeology
* Knot of Isis (tyet), symbol of welfare/life.
* Minoan snake goddess figurines#Sacral knot
Arts, entertainme ...
''K''
1 and ''K''
2 along an (''n'' + 1)-dimensional 1-handle ''h'' called a ''band'' is an ''n''-dimensional knot ''K'' such that:
* There is an (''n'' + 1)-dimensional 1-handle ''h'' connected to (''K''
1, ''K''
2) embedded in ''S''
''n''+2.
* There are points
and
such that
is attached to
along
.
''K'' is the ''n''-dimensional knot obtained by this surgery.
A band sum is thus a generalization of the usual
connected sum
In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classifi ...
of knots.
See also
*
Manifold decomposition
In topology, a branch of mathematics, a manifold ''M'' may be decomposed or split by writing ''M'' as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form ''M''.
Manifo ...
References
*.
*.
Topology
Differential topology
Knot theory
Operations on structures
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