# Are period domains ever contractible

Which simply-connected period domains are contractible?

Examples. Siegel upper-half space? Poincare upper-half plane? Universal cover of a Shimura variety?

Are these contractible?

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"half-space", "half-plane": what do you think? –  Francesco Polizzi Apr 11 '13 at 11:43
@Jason S: I am also a Jason S! –  Jason Starr Apr 11 '13 at 12:01
I would like to know the answer for the universal cover of a Shimura variety. But maybe this would be more obvious if one could remember the definition of Shimura variety off the top of one's head. –  dhagbert Apr 11 '13 at 12:25
dhagbert: see mathoverflow.net/questions/67699 ... –  Dan Petersen Apr 11 '13 at 12:31

The universal cover of a Shimura variety is a bounded symmetric domain (that's part of the definition), and these are listed in the Wikipedia (under Hermitian symmetric spaces), so you can check this for yourself.

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