In the process of attaching a 
-handle to a manifold 
, the boundary of 
is modified by a process called 
-surgery. Surgery consists of the removal of a tubular
neighborhood of a 
-sphere 
from the boundaries of 
and the 
standard sphere, and the gluing together of these two
scarred-up objects along their common boundaries.
Surgery
See also
Boundary, Dehn Surgery, Handle, Manifold, Sphere, Tubular NeighborhoodExplore with Wolfram|Alpha
References
Cappell, S.; Ranicki, A.; and Rosenberg, J. (Eds.). Surveys on Surgery Theory, Vol. 1. Princeton, NJ: Princeton University Press, 2000.Referenced on Wolfram|Alpha
SurgeryCite this as:
Weisstein, Eric W. "Surgery." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Surgery.html