Band sum
Encyclopedia
In geometric topology
, a band sum of two n-dimensional knots K1 and K2 along an (n + 1)-dimensional 1-handle h called a band is an n-dimensional knot K such that:
K is the n-dimensional knot obtained by this surgery.
A band sum is thus a generalization of the usual connected sum
of knots.
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
, a band sum of two n-dimensional knots K1 and K2 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 (K1, K2) embedded in Sn+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
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...
of knots.