= One-handle
{title2=$D^1\times D^{n-1}$}
A <one-handle> on an $n$-dimensional <manifold with boundary> is $D^1\times D^{n-1}$ attached along $S^0\times D^{n-1}$, two disjoint boundary disks. In <dimension> two it is a band joined along its two ends; depending on the attachment it can connect components or create a new loop. The core is $D^1\times\{0\}$ and the <belt sphere> is $\{0\}\times S^{n-2}$. The attachment data, including how the two ends are identified with the old boundary, is part of the construction.
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