Connected manifold with disconnected boundary?

Is there any simple example of a connected manifold with disconnected boundary?

• Perhaps an open-ended cylinder? – Thomas Andrews Jan 17 '15 at 16:21
• Or just $[0..1]$. (I don’t get that cylinder-example, though @ThomasAndrews.) – k.stm Jan 17 '15 at 16:23
• It's just $S^1\times [0,1]$, @k.stm – Thomas Andrews Jan 17 '15 at 16:26
• @ThomasAndrews Ah. How is this “open-ended”? – k.stm Jan 17 '15 at 16:27
• You guys read too much math, not enough common language. Google "open-ended cylinder" and all the early usages are describing uncapped cylinders. Basically, toilet paper rolls. @k.stm – Thomas Andrews Jan 17 '15 at 16:34

Not only are there many connected manifolds with disconnected boundaries (such as $[0,1]$ or a cylinder), there is an equivalence relation built on it called cobordism, where two manifolds are said to be cobordant if their disjoint union is the boundary of a manifold one dimension higher. Technically, the higher dimensional manifold need not be connected, but this is often the case.