Why can't you map your app to the root context?
You could (in theory) deploy the app to both /a and /b, but internally they would be "different" apps.
You also can't readily map /b to /a. You can't even do something clever like put a filter in "/b" that simply forwards to the corresponding url in /a, because you can't forward across applications -- you could redirect, but that's not the same thing.
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