Abstract
In this talk I will describe two examples of application of topology tophysics. The first one refers to attempts to understand the spin-statisticsconnection in the non-relativistic context. This naturally leads to theconsideration of quantum mechanics on topologically non-trivialconfigurations spaces. The second one has to do with the possibility ofrelating certain topological invariants to quantum systems that present aquantum phase transition. In particular I will show how, in the case of theanisotropic XY-model, it is possible to actually compute these invariantsand relate their dependence on the external field to the quantum phasetransition.
