| Résume | I will start by talking about moduli spaces of 0-dimensional submanifolds - which are just configuration spaces - and how one can study their homology by the method of stabilisation. In outline, this method entails taking the limit as the number of points in the configuration goes to infinity, calculating the homology there, and then relating this back to the original configuration spaces. This last step is what is known as homological stability. I will then explain what is known when we consider moduli spaces where the submanifolds have higher (i.e., positive) dimension - for example spaces of oriented subsurfaces or spaces of links - and what is still unknown. |
