(Unoriented) Gopakumar-Vafa invariants

After a review of topological string theory and BPS invariants, I will discuss the type IIA physical realisation of the unoriented topological string introduced by Walcher, its M-theory lift, and I will show how it allows to compute open and unoriented topological amplitudes in terms of one-loop diagrams of BPS\M2-brane states.