Doctor of Philosophy
In this thesis, we study 4-dimensional weighted projective spaces and homotopy properties of their symplectomorphism groups. Using these computations, we also investigate some homotopy theoretic properties of a few associated embedding spaces. In the classical case of the complex projective plane, Gromov observed that its symplectomorphism group is homotopy equivalent to its subgroup of Kahler isometries. We find that in the case of one singularity, the symplectomorphism group is weakly homotopy equivalent to the Kahler isometry group of a certain Hirzebruch surface, which corresponds to the resolution of the singularity. In the case of multiple singularities, the symplectomorphism groups are weakly equivalent to tori. These computations then allow us to investigate some properties of related embedding spaces.
VanHoof, Martin L., "Symplectomorphism Groups of Weighted Projective Spaces and Related Embedding Spaces" (2013). Electronic Thesis and Dissertation Repository. 1868.