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: There is an (n + 1)-dimensional 1-handle h connected to (K1, K2) embedded in Sn+2. There are points p 1 ∈ K 1 {\displaystyle p_{1}\in K_{1}} and p 2 ∈ K 2 {\displaystyle p_{2}\in K_{2}} such that h {\displaystyle h} is attached to K 1 ⊔ K 2 {\displaystyle K_{1}\sqcup K_{2}} along p 1 ⊔ p 2 {\displaystyle p_{1}\sqcup p_{2}} .
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: There is an (n + 1)-dimensional 1-handle h connected to (K1, K2) embedded in Sn+2. There are points p 1 ∈ K 1 {\displaystyle p_{1}\in K_{1}} and p 2 ∈ K 2 {\displaystyle p_{2}\in K_{2}} such that h {\displaystyle h} is attached to K 1 ⊔ K 2 {\displaystyle K_{1}\sqcup K_{2}} along p 1 ⊔ p 2 {\displaystyle p_{1}\sqcup p_{2}} .
Source: Wikipedia "Band sum" · CC BY-SA 4.0
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