Tyrone Ghaswala, Department of Pure Mathematics, University of Waterloo
"The liftable mapping class group"
This thesis studies a subgroup of the mapping class group related to a covering space, called the liftable mapping class group. This thesis covers the following results. A classification of cyclic branched covers of the sphere with the property that the liftable mapping class group coincides with the entire mapping class group. Group presentations for the liftable mapping class group corresponding to a family of cyclic branched covers of the sphere called the balanced superelliptic covers, and a family of cyclic branched covers of the torus. A characterisation of the liftable mapping class group for surfaces with boundary.
MC 2009