Alternating links on surfaces

Classical alternating links have nice hyperbolic geometric properties. Recently, Howie and Purcell studied hyperbolicity of alternating links on orientable surfaces in 3-manifolds. In this thesis, we generalise Howie and Purcell's alternating links on nonorientable projection surfaces. As an application, we study Klein bottly alternating links in prism manifolds. In the way, we utilize the chunk decomposition developed by Howie-Purcell rooted from Menasco-Thurston’s 1980s work. Another widely used method of studying the geometry of the link exterior is the octahedral decomposition, first implemented by Weeks in his 1985 thesis and further used by Sakuma-Yokota. In the last part of the thesis, we elaborate how the octahedral decomposition can be used to study links in thickened surfaces.