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Topology of the diffeomorphism group

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electroweak
#1
Feb25-12, 07:19 PM
P: 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?
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Office_Shredder
#2
Feb25-12, 08:20 PM
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PF Gold
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http://en.wikipedia.org/wiki/Diffeomorphism#Topology
quasar987
#3
Feb26-12, 08:20 AM
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PF Gold
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The classical reference is

Augustin Bangaya, The Structure of Classical Diffeomorphism Groups


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