How come you can turn a T-shirt inside out?

The **automorphism group** of a **3-times punctured sphere** has 12 path-components (12 elements up to isotopy). There are 6 elements that preserve orientation, and 6 that reverse. In particular** the orientation-reversing automorphisms reverse the orientation of all the boundary circles**.

File this one under things I want to understand.

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Tags: alebraic topology, algebraic topology, automorphic, automorphism, automorphisms, automorphismsautomo, basic facts, clothing, common sense, facts, group theory, groups, logic, math, mathematics, maths, rphism groups, topology, why

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