A filled torus (a doughnut) is a 3-manifold homeomorphic to \(S^1 \times D^2\), where \(D^2\) is the 2-dimensional disk. There exists a deformation retract from the doughnut to a circle, so the fundamental group of the doughnut is \(\pi_1(S^1 \times D^2) \cong \mathbb{Z}\).
M4 is also powerful for AI, with faster memory bandwidth and an incredibly fast Neural Engine — benefiting everyone from college students transcribing lecture notes, to creators storyboarding a new project, to business users polishing emails. With the new iPad Air, unified memory jumps 50 percent, to 12GB, and memory bandwidth increases to 120GB/s, helping users run AI models faster. The 16-core Neural Engine is 3x faster than that of M1 and is perfect for everyday tasks that use on-device AI, like searching for subjects and texts in photos, or leveraging powerful AI features in apps like Goodnotes and Onform: Video Analysis App.2 The Neural Engine also powers capabilities in Apple Creator Studio apps, like removing the background of video footage with Scene Removal Mask in Final Cut Pro.
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