MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
"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 ... – 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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.