A gentle introduction to Kirby calculus

I will be taking us on a journey through low dimensional topology, starting in 2 dimensions motivating handles decompositions in a dimension that we can visualize, moving onto to a brief of note of what this means in 3 dimensions and then moving onto the wild world of 4 manifolds. I will be showing a way in which we can actually try and view a 4 manifold before moving onto a way of manipulating these diagrams to give diffeomorphic 4 manifolds. Hopefully, I will have time to go into some ways in which Kirby calculus has been used to show that certain potential exotic 4 spheres are not exotic and some results on stable diffeomorphims of 4 manifolds.