>Is it possible, using asynchronous connections or by some other method, that when I issue a TableUpdate, the user will not have to wait for the trigger to fire and complete?
You could use an async connection to issue the command but remember, the trigger is considered part of the command. You cannot seperate then. They exist in the same transaction.
I agree with Sergey. If you client will allow for some latency, schedule a process to update aggregated values.
-Mike