Handle decomposition
= Handle decomposition
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A handle decomposition builds an $n$-dimensional <manifold> by successively adjoining $D^h\times D^{n-h}$ along $S^{h-1}\times D^{n-h}$. The attaching data comprise an <attaching sphere> and its <framing of an embedded sphere>. Reading a decomposition backwards replaces index $h$ by index $n-h$ and interchanges its <attaching spheres> and <belt spheres>.