Definition:Handle

Definition

A handle is a homeomorphic copy of the cylinder:

$\set {\tuple {x_1, x_2, x_3} \in \R^3: {x_1}^2 + {x_2}^2 = 1, \size {x_3} \le 1}$

such that the two circles $x_3 = 1$ are identified with the boundary circles of two discs removed from the sphere $\Bbb S^2$.

Also see

• Results about handles can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): handle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): handle