{{Short description|Method of connecting knots}} In geometric topology, a '''band sum''' of two ''n''-dimensional knots ''K''<sub>1</sub> and ''K''<sub>2</sub> 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''<sub>1</sub>, ''K''<sub>2</sub>) embedded in ''S''<sup>''n''+2</sup>. * There are points <math>p_1\in K_1</math> and <math>p_2\in K_2</math> such that <math>h</math> is attached to <math>K_1\sqcup K_2</math> along <math>p_1\sqcup p_2</math>.
''K'' is the ''n''-dimensional knot obtained by this surgery.
A band sum is thus a generalization of the usual connected sum of knots.
==See also== *Manifold decomposition
==References== *{{citation|title=Knots and Links|first=Peter R.|last=Cromwell|publisher=Cambridge University Press|year=2004|isbn=9780521548311|page=90|url=https://books.google.com/books?id=djvbTNR2dCwC&pg=PA90}}. *{{citation|title=Survey on Knot Theory|first=Akio|last=Kawauchi|publisher=Springer|year=1996|isbn=9783764351243|page=31|url=https://books.google.com/books?id=gWbyJn7c5G0C&pg=PA31}}.
Category:Topology Category:Differential topology Category:Knot theory Category:Operations on structures
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