I second that you just need a wicking tank top for indoor training. You are not traveling a distance around that you need the pockets of a jersey.
But where am I going to put the remote control for the TV?
Seriously, I don't own any workout tank tops, and only a couple of wicking t-shirts, so it's less expense to just wear my summer jerseys. I won't be working out sans shirt anytime soon, even in my own house.