Topology of the diffeomorphism group

1. electroweak

44
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?

2. Office_Shredder

4,499
Staff Emeritus
3. quasar987

4,774
The classical reference is

Augustin Bangaya, The Structure of Classical Diffeomorphism Groups