I read some text to find it's definition(adsbygoogle = window.adsbygoogle || []).push({});

Is it possible to tell me it's definition?

I read below statements about local and global geometry and I didn't understand it. is it possible tell me it.

"If M ( a manifold) has a trivial topology, a single neighborhood can be extended globally, and geometry is indeed trivial; but if M contains non-contractible curves, such as extension may not be possible."

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# Contractible curves

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