I would like to study the path components (isotopy classes) of the diffeomorphism group of some compact Riemann surface. To make sense of path connectedness, I require a notion of continuity; hence, I require a notion of an open set of diffeomorphisms. What sort of topology should I put on the diffeomorphism group?(adsbygoogle = window.adsbygoogle || []).push({});

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# Topology of the diffeomorphism group

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