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Date: 7-6-2021
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Date: 29-7-2021
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Date: 10-6-2021
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The connected sum of
-manifolds
and
is formed by deleting the interiors of
-balls
in
and attaching the resulting punctured manifolds
to each other by a homeomorphism
, so
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is required to be interior to
and
bicollared in
to ensure that the connected sum is a manifold.
Topologically, if and
are pathwise-connected, then the connected sum is independent of the choice of locations on
and
where the connection is glued.
The illustrations above show the connected sums of two tori (top figure) and of two pairs of multi-handled tori.
The connected sum of two knots is called a knot sum.
REFERENCES:
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 39, 1976.
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