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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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    $\begingroup$ "half-space", "half-plane": what do you think? $\endgroup$
    – Francesco Polizzi
    Commented Apr 11, 2013 at 11:43
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    $\begingroup$ @Jason S: I am also a Jason S! $\endgroup$
    – Jason Starr
    Commented Apr 11, 2013 at 12:01
  • $\begingroup$ 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. $\endgroup$
    – dhagbert
    Commented Apr 11, 2013 at 12:25
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    $\begingroup$ dhagbert: see mathoverflow.net/questions/67699 ... $\endgroup$
    – Dan Petersen
    Commented Apr 11, 2013 at 12:31

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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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