Your other option is for you to call someone in to determine what it is and then request your landlord take on the removal.
The real question: is the asbestos creating a health hazard?
Check out the American Lung Association site: http://www.lung.org/lung-disease/asbestosis/understanding-as
If it's encapsulated, like in the flooring underlayment, then it's really unlikely to be a problem. If it's lining the ducts, yeah, it could be a problem.
For most people, asbestos is housing is benign. The part about "The severity of your disease depends on how long you were exposed to asbestos and the amount you inhaled"? Asbestos workers who spent forty hours fifty weeks a year and also smoked are the most likely people to be affected. People sitting at home watching TV, not so likely to be affected.