topology of the diffeomorphism group

electroweak

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?

Office_Shredder

http://en.wikipedia.org/wiki/Diffeomorphism#Topology

quasar987

The classical reference is

Augustin Bangaya, The Structure of Classical Diffeomorphism Groups

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electroweak	topology of the diffeomorphism group Tweet 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?

Office_Shredder Blog Entries: 1 Recognitions: Homework Help	http://en.wikipedia.org/wiki/Diffeomorphism#Topology

quasar987 Recognitions: Gold Member Homework Help Science Advisor	The classical reference is Augustin Bangaya, The Structure of Classical Diffeomorphism Groups